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main.cpp
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main.cpp
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/*******************************************************************************************************/
/* */
/* CTMRG code for 2D classical models */
/* */
/*******************************************************************************************************/
/*******************************************************************************************************/
/* */
/* main.cpp */
/* CTMRG */
/* version 0.1 */
/* */
/* This code is CTMRG algorithm for 2D classical models (Ising, Clock, Potts) */
/* Copyright (C) 2016 Jozef Genzor <jozef.genzor@gmail.com> */
/* */
/* */
/* This file is part of CTMRG. */
/* */
/* CTMRG is free software: you can redistribute it and/or modify */
/* it under the terms of the GNU General Public License as published by */
/* the Free Software Foundation, either version 3 of the License, or */
/* (at your option) any later version. */
/* */
/* CTMRG is distributed in the hope that it will be useful, */
/* but WITHOUT ANY WARRANTY; without even the implied warranty of */
/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the */
/* GNU General Public License for more details. */
/* */
/* You should have received a copy of the GNU General Public License */
/* along with CTMRG. If not, see <http://www.gnu.org/licenses/>. */
/* */
/*******************************************************************************************************/
/*
* This code is an implementation of the CTMRG algorithm introduced in the articles:
*
* Corner Transfer Matrix Renormalization Group Method
* J. Phys. Soc. Jpn. 65, pp. 891-894 (1996)
* http://arxiv.org/abs/cond-mat/9507087v5
*
* Corner Transfer Matrix Algorithm for Classical Renormalization Group
* J. Phys. Soc. Jpn. 66, pp. 3040-3047 (1997)
* http://arxiv.org/abs/cond-mat/9705072
*
* For linear algebra (matrix diagonalization in particular),
* Eigen library (3.2.7) is called.
*
* Compilation under Mac:
*
* g++ -m64 -O3 -I/.../Eigen main.cpp -o main.x
*
*/
/*******************************************************************************************************/
#include <stdlib.h>
#include <stdio.h>
#include <iostream>
#include <math.h>
#include <time.h>
#include <vector>
#define NDEBUG
#include "SVD"
#include "Eigenvalues"
using namespace Eigen;
const double pi = asin(1.0)*2;
/*******************************************************************************************************/
/*******************************************************************************************************/
void Initialize(const int & q, const int & model, const double & h, const double & g,
const double & temperature, double * const W_B, double * const T, double * const C);
MatrixXd Create_DM(const int & q, const int & n, const double * const C);
int Increase(const int & q, const int & m, const int & n);
void Diagonalize_DM(const int & q, const int & n, const int & m, const int & mn, const MatrixXd & DM, double * const E, double * const * const P);
void Extend_and_renormalize_TM(const int & q, const int & n, const int & mn, const double * const T, const double* const W_B,
const double * const * const P, double * const Theta_2, double * const T_new);
void Extend_and_renormalize_CTM(const int & q, const int & n, const int & mn, const double * const T, const double * const C,
const double * const * const P, const double * const Theta_2, double * const C_new);
void Normalize_T(const int & q, const int & mn, const double * const T_new, double * const T, std::vector<double> & log_beta);
void Normalize_C(const int & q, const int & mn, const double * const C_new, double * const C, std::vector<double> & log_alpha);
double Calculate_mag(const int & q, const int & model, const int & n, const MatrixXd & DM);
double Calculate_entropy(const int & q, const int & n, const double * const E);
double Trace_C4(const int & q, const int & n, const double * const C);
double Calculate_U(const int & q, const int & model, const int & n, const double * const C, const double * const T);
double Calculate_F(const int & q, const int & i, const int & n, const double & temperature, const double * const C,
const std::vector<double> & log_beta, const std::vector<double> & log_alpha);
double H1_Ising(const int &, const double & h, const int & s_1, const int & s_2, const int & s_3, const int & s_4);
double H2_Ising(const int &, const double & h, const double & g, const int & s_1, const int & s_2, const int & s_3, const int & s_4);
double H3_Ising(const int &, const double & h, const double & g, const int & s_1, const int & s_2, const int & s_3, const int & s_4);
double H1_Clock(const int & q, const double & h, const int & s_1, const int & s_2, const int & s_3, const int & s_4);
double H2_Clock(const int & q, const double & h, const double & g, const int & s_1, const int & s_2, const int & s_3, const int & s_4);
double H3_Clock(const int & q, const double & h, const double & g, const int & s_1, const int & s_2, const int & s_3, const int & s_4);
double H1_Potts(const int &, const double & h, const int & s_1, const int & s_2, const int & s_3, const int & s_4);
double H2_Potts(const int &, const double & h, const double & g, const int & s_1, const int & s_2, const int & s_3, const int & s_4);
double H3_Potts(const int &, const double & h, const double & g, const int & s_1, const int & s_2, const int & s_3, const int & s_4);
double deltaFunc(const int & i, const int & j);
/*******************************************************************************************************/
/*******************************************************************************************************/
int main ()
{
clock_t start, end;
double runTime;
start = clock(); //time measurement start
int model_r;
int q_r;
double h_r;
double initial_r;
double final_r;
double delta_r;
int m_r;
int L_r;
double g_r;
double LIMIT_M_r;
double LIMIT_U_r;
double LIMIT_F_r;
double LIMIT_fF_r;
FILE* par;
par = fopen("INIT.txt", "r");
if ( par == NULL )
{
printf("Can't open the input file \"INIT.txt\" \n");
return 1;
}
fscanf(par, "%d%*[^\n]", &model_r);
fscanf(par, "%d%*[^\n]", &q_r);
fscanf(par, "%lf%*[^\n]", &h_r);
fscanf(par, "%lf%*[^\n]", &initial_r);
fscanf(par, "%lf%*[^\n]", &final_r);
fscanf(par, "%lf%*[^\n]", &delta_r);
fscanf(par, "%d%*[^\n]", &m_r);
fscanf(par, "%d%*[^\n]", &L_r);
fscanf(par, "%lf%*[^\n]", &g_r);
fscanf(par, "%lf%*[^\n]", &LIMIT_M_r);
fscanf(par, "%lf%*[^\n]", &LIMIT_U_r);
fscanf(par, "%lf%*[^\n]", &LIMIT_F_r);
fscanf(par, "%lf%*[^\n]", &LIMIT_fF_r);
fclose(par);
const int model = model_r; //0 (Ising), 1 (Clock), 2 (Potts)
if ( model==0 ) // for Ising
{
q_r = 2;
}
const int q = q_r;
const double h = h_r; //1.E-14;
const double initial = initial_r;
const double final = final_r;
const double delta = delta_r;
const int m = m_r;
const int L = L_r; //maximal lattice size (i <= L)
const double g = g_r; //symmetry breaking term (external magnetic field on the boundary)
const double LIMIT_M = LIMIT_M_r; //precision for magnetization
const double LIMIT_U = LIMIT_U_r; //precision for inner energy
const double LIMIT_F = LIMIT_F_r; //precision for free energy - it converges very, very slow
const double LIMIT_fF = LIMIT_fF_r; //precision for free energy - fast converging
if ( model != 0 && model != 1 && model != 2 )
{
std::cout << "choose correct value for Ising (0), Clock (1) or Potts (2) in INIT.txt" << std::endl;
abort();
}
switch (model)
{
case 0:
printf("# Ising model\n");
break;
case 1:
printf("# %d-states Clock model\n", q);
break;
case 2:
printf("# %d-states Potts model\n", q);
break;
}
printf("# h = %1E\t\tg = %1E\t\tm = %d\t\tL_max = %d\n", h, g, m, L);
FILE* fw;
if ((fw = fopen("DATA.txt", "w")) == NULL) //this creates file DATA.txt
{
printf("Can't open the output file \"DATA.txt\" \n");
return 1;
}
fclose(fw);
fw = fopen("DATA.txt","a");
switch (model)
{
case 0:
fprintf(fw, "# Ising model\n");
break;
case 1:
fprintf(fw, "# %d-states Clock model\n", q);
break;
case 2:
fprintf(fw, "# %d-states Potts model\n", q);
break;
}
fprintf(fw, "# m=%d, L_max=%d, h=%1E, g=%1E\n", m, L, h, g);
fprintf(fw, "# Temp\t\tMagnetization\t\tInternal energy\t\tFree energy\t\tFast free energy\tEntropy\t\t\t\tIter\n");
fclose(fw);
printf("# Temp\t\tMagnetization\t\tInternal energy\t\tFree energy\t\tFast free energy\tEntropy\t\t\t\tIter\n");
double temperature;
for (temperature = initial; temperature <= final; temperature += delta)
{
int i = 3; //actual lattice size (i x i) within each iteration, start with 3x3
int n = q; //degrees of freedom counting - we start with n=q
double *W_B;
double *T;
double *C;
W_B = (double *)malloc(q*q*q*q*sizeof(double)); //Boltzman weight
T = (double *)malloc(q*q*m*m*sizeof(double)); //transfer matrix (half-row or half-column)
C = (double *)malloc(q*m*m*sizeof(double)); //corner transfer matrix
Initialize(q, model, h, g, temperature, W_B, T, C);
double entropy = 0;
int numb_of_iter = 0; //number of required iterations
//magnetization
double mag_new = 0;
double mag_prev = 1;
//free energy
double free_energy_new = 0;
double free_energy_prev = 1;
double free_energy_fast_new = 0;
double free_energy_fast_prev = 1;
std::vector<double> log_beta; //this vector will store logarithms of normalization coefficients for T
log_beta.push_back(0); //T from Initialize() is not normalized, thus first beta=1, and log(beta) = 0
std::vector<double> log_alpha; //this vector will store logarithms of normalization coefficients for C
log_alpha.push_back(0); //C from Initialize() is not normalized, thus first alpha=1 and log(alpha) = 0
//internal energy
double U_new = 0;
double U_prev = 1;
while (((((fabs(mag_new - mag_prev) > LIMIT_M)) ||
( fabs(U_new - U_prev) > LIMIT_U) ||
( fabs(free_energy_new - free_energy_prev) > LIMIT_F) ||
( fabs(free_energy_fast_new - free_energy_fast_prev) > LIMIT_fF))
&& (i <= L) ) || (i<=5) )
{
free_energy_prev = free_energy_new;
free_energy_new = Calculate_F(q, i, n, temperature, C, log_beta, log_alpha);
free_energy_fast_prev = free_energy_fast_new;
free_energy_fast_new = - temperature * log_beta[ (i-1)/2 - 1 ];
U_prev = U_new;
U_new = Calculate_U(q, model, n, C, T); //U_new is inner energy
MatrixXd* pDM = new MatrixXd(Create_DM(q, n, C)); //density matrix creation - by multiplying four C matrices
mag_prev = mag_new;
mag_new = Calculate_mag(q, model, n, *pDM);
int mn = Increase(q, m, n);
double *E;
E = (double *)malloc(q*n*sizeof(double)); //eigenvalues
double *P[q*n]; //projection operator
for (int j=0; j<q*n; j++)
{
P[j]=(double *)malloc(mn*sizeof(double));
}
Diagonalize_DM(q, n, m, mn, *pDM, E, P);
delete pDM;
pDM = NULL;
entropy = Calculate_entropy(q, n, E);
free((void *) E);
E = NULL;
double *Theta_2;
Theta_2 = (double *)malloc(q*q*q*mn*n*sizeof(double)); //auxiliary array
double *T_new;
T_new = (double *)malloc(q*q*mn*mn*sizeof(double));
Extend_and_renormalize_TM(q, n, mn, T, W_B, P, Theta_2, T_new);
double *C_new;
C_new = (double *)malloc(q*mn*mn*sizeof(double));
Extend_and_renormalize_CTM(q, n, mn, T, C, P, Theta_2, C_new);
free((void *) Theta_2);
Theta_2 = NULL;
for (int j=0; j<q*n; j++)
{
free(P[j]);
P[j]=NULL;
}
Normalize_T(q, mn, T_new, T, log_beta); //normalizing T - dividing by the largest element of array T_new
free((void *) T_new);
T_new = NULL;
Normalize_C(q, mn, C_new, C, log_alpha); //normalizing C - dividing by the largest element of array C_new
free((void *) C_new);
C_new = NULL;
n = mn; //increasing n
numb_of_iter = (i-1)/2;
printf("%1.6E\t%1.16E\t%1.16E\t%1.16E\t%1.16E\t%1.16E\t\t%d\n",
temperature, mag_new, U_new, free_energy_new, free_energy_fast_new, entropy, numb_of_iter);
i += 2; //lattice size increasing
}
free((void *) W_B);
W_B = NULL;
free((void *) T);
T = NULL;
free((void *) C);
C = NULL;
fw = fopen("DATA.txt","a");
fprintf(fw, "%1.6E\t%1.16E\t%1.16E\t%1.16E\t%1.16E\t%1.16E\t\t%d\n",
temperature, mag_new, U_new, free_energy_new, free_energy_fast_new, entropy, numb_of_iter);
fclose(fw);
}
end = clock(); //time measurement end
runTime = (end - start) / (double) CLOCKS_PER_SEC ;
printf ("Run time is %f seconds\n", runTime);
return 0;
}
/*******************************************************************************************************/
/*******************************************************************************************************/
void Initialize(const int & q, const int & model, const double & h, const double & g, const double & temperature,
double * const W_B, double * const T, double * const C)
{
double (* pFunc1)(const int &, const double &, const int &, const int &, const int &, const int &) = NULL;
double (* pFunc2)(const int &, const double &, const double &, const int &, const int &, const int &, const int &) = NULL;
double (* pFunc3)(const int &, const double &, const double &, const int &, const int &, const int &, const int &) = NULL;
switch (model)
{
case 0:
pFunc1 = &H1_Ising;
pFunc2 = &H2_Ising;
pFunc3 = &H3_Ising;
break;
case 1:
pFunc1 = &H1_Clock;
pFunc2 = &H2_Clock;
pFunc3 = &H3_Clock;
break;
case 2:
pFunc1 = &H1_Potts;
pFunc2 = &H2_Potts;
pFunc3 = &H3_Potts;
break;
}
double sum;
for (int s_1=0; s_1<q; s_1++)
{
for (int s_2=0; s_2<q; s_2++)
{
for (int s_4=0; s_4<q; s_4++)
{
sum = 0;
for (int s_3=0; s_3<q; s_3++)
{
W_B[q*q*q*s_1 + q*q*s_2 + q*s_3 + s_4] = exp( - (*pFunc1)(q, h, s_1, s_2, s_3, s_4)/temperature );
T[q*q*q*s_1 + q*q*s_2 + q*s_3 + s_4] = exp( - (*pFunc2)(q, h, g, s_1, s_2, s_3, s_4)/temperature );
sum += exp( - (*pFunc3)(q, h, g, s_1, s_2, s_3, s_4)/temperature );
}
C[q*q*s_1 + q*s_2 + s_4] = sum;
}
}
}
}
MatrixXd Create_DM(const int & q, const int & n, const double * const C)
{
double sum;
double *AX;
AX = (double *)malloc(q*n*n*sizeof(double));
/* auxiliary array AX initialization */
for (int x=0; x<q; x++)
{
for (int a=0; a<n; a++)
{
for (int c=0; c<n; c++)
{
sum = 0;
for (int b=0; b<n; b++)
{
sum += C[n*n*x + n*a + b]*C[n*n*x + n*b + c];
}
AX[n*n*x + n*a + c] = sum;
}
}
}
/* normalization of AX */
double norm;
norm = 0.0;
for (int j=0; j<q*n*n; j++)
{
norm += AX[j]*AX[j];
}
norm = sqrt(norm);
for (int j=0; j<q*n*n; j++)
{
AX[j] /= norm;
}
MatrixXd DM(q*n, q*n);
for (int c=0; c<n; c++)
{
for (int x=0; x<q; x++)
{
for (int d=0; d<n; d++)
{
for (int y=0; y<q; y++)
{
sum = 0;
for (int a=0; a<n; a++)
{
sum += AX[n*n*x + n*a + c]*AX[n*n*y + n*a + d];
}
DM(q*c + x, q*d + y) = sum;
}
}
}
}
free((void *) AX);
AX = NULL;
return DM;
}
void Diagonalize_DM(const int & q, const int & n, const int & m, const int & mn, const MatrixXd & DM, double * const E, double * const * const P)
{
/* DM diagonalization */
SelfAdjointEigenSolver<MatrixXd> ES(DM);
MatrixXd V = ES.eigenvectors();
//MatrixXd D = ES.eigenvalues().asDiagonal();
for (int i=0; i<(q*n); i++)
{
E[i] = ES.eigenvalues()(i);
}
if (q*n <= m)
{
for (int j=0; j<(q*n); j++)
{
for (int k=0; k<(q*n); k++)
{
P[j][k] = ES.eigenvectors()(j,k);
}
}
}
else
{
for (int j=0; j<(q*n); j++)
{
for (int k=0; k<mn; k++)
{
P[j][k] = ES.eigenvectors()(j, k + q*n - mn); //this corresponds to the mn largest eigenvalues
}
}
}
}
void Extend_and_renormalize_TM(const int & q, const int & n, const int & mn, const double * const T, const double* const W_B,
const double * const * const P, double * const Theta_2, double * const T_new)
{
double *Theta_1;
Theta_1 = (double *)malloc(q*q*mn*n*sizeof(double)); //auxiliary array
double sum;
for (int xi = 0; xi < q; xi++)
{
for (int Xi = 0; Xi < n; Xi++)
{
for (int Sigma_p = 0; Sigma_p < mn; Sigma_p++)
{
for (int sigma = 0; sigma < q; sigma++)
{
sum = 0;
for (int Sigma = 0; Sigma < n; Sigma++)
{
sum += T[q*n*n*sigma + q*n*Sigma + q*Xi + xi]*P[q*Sigma + sigma][Sigma_p];
}
Theta_1[q*mn*n*sigma + q*n*Sigma_p + q*Xi + xi] = sum;
}
}
}
}
for (int sigma_p = 0; sigma_p < q; sigma_p++)
{
for (int Sigma_p = 0; Sigma_p < mn; Sigma_p++)
{
for (int Xi = 0; Xi < n; Xi++)
{
for (int xi = 0; xi < q; xi++)
{
for (int xi_p = 0; xi_p < q; xi_p++)
{
sum = 0;
for (int sigma = 0; sigma < q; sigma++)
{
sum += W_B[q*q*q*sigma_p + q*q*sigma + q*xi + xi_p]*Theta_1[q*mn*n*sigma + q*n*Sigma_p + q*Xi + xi];
}
Theta_2[q*q*mn*n*sigma_p + q*q*n*Sigma_p + q*q*Xi + q*xi + xi_p] = sum;
}
}
}
}
}
free((void *) Theta_1);
Theta_1 = NULL;
for (int sigma_p = 0; sigma_p < q; sigma_p++)
{
for (int Sigma_p = 0; Sigma_p < mn; Sigma_p++)
{
for (int Xi_p = 0; Xi_p < mn; Xi_p++)
{
for (int xi_p = 0; xi_p < q; xi_p++)
{
sum = 0;
for (int xi = 0; xi < q; xi++)
{
for (int Xi = 0; Xi < n; Xi++)
{
sum += P[q*Xi + xi][Xi_p]*Theta_2[q*q*mn*n*sigma_p + q*q*n*Sigma_p + q*q*Xi + q*xi + xi_p];
}
}
T_new[q*mn*mn*sigma_p + q*mn*Sigma_p + q*Xi_p + xi_p] = sum;
}
}
}
}
}
void Extend_and_renormalize_CTM(const int & q, const int & n, const int & mn, const double * const T, const double * const C,
const double * const * const P, const double * const Theta_2, double * const C_new)
{
double *Theta_3;
Theta_3 = (double *)malloc(q*q*q*mn*n*sizeof(double)); //auxiliary array
double sum = 0;
for (int sigma_p = 0; sigma_p < q; sigma_p++)
{
for (int Sigma_p = 0; Sigma_p < mn; Sigma_p++)
{
for (int Sigma_pp = 0; Sigma_pp < n; Sigma_pp++)
{
for (int xi = 0; xi < q; xi++)
{
for (int xi_p = 0; xi_p < q; xi_p++)
{
sum = 0;
for (int Xi = 0; Xi < n; Xi++)
{
sum +=
Theta_2[q*q*mn*n*sigma_p + q*q*n*Sigma_p + q*q*Xi + q*xi + xi_p]
*C[n*n*xi + n*Xi + Sigma_pp];
}
Theta_3[q*q*mn*n*sigma_p + q*q*n*Sigma_p + q*q*Sigma_pp + q*xi + xi_p] = sum;
}
}
}
}
}
double *Theta_4;
Theta_4 = (double *)malloc(q*q*mn*n*sizeof(double)); //auxiliary array
for (int sigma_p = 0; sigma_p < q; sigma_p++)
{
for (int Sigma_p = 0; Sigma_p < mn; Sigma_p++)
{
for (int Xi_pp = 0; Xi_pp < n; Xi_pp++)
{
for (int xi_p = 0; xi_p < q; xi_p++)
{
sum = 0;
for (int xi = 0; xi < q; xi++)
{
for (int Sigma_pp = 0; Sigma_pp < n; Sigma_pp++)
{
sum +=
Theta_3[q*q*mn*n*sigma_p + q*q*n*Sigma_p + q*q*Sigma_pp + q*xi + xi_p]
*T[q*n*n*xi + q*n*Sigma_pp + q*Xi_pp + xi_p];
}
}
Theta_4[q*mn*n*sigma_p + q*n*Sigma_p + q*Xi_pp + xi_p] = sum;
}
}
}
}
free((void *) Theta_3);
Theta_3 = NULL;
for (int sigma_p = 0; sigma_p < q; sigma_p++)
{
for (int Sigma_p = 0; Sigma_p < mn; Sigma_p++)
{
for (int Xi_p = 0; Xi_p < mn; Xi_p++)
{
sum = 0;
for (int xi_p = 0; xi_p < q; xi_p++)
{
for (int Xi_pp = 0; Xi_pp < n; Xi_pp++)
{
sum += P[q*Xi_pp + xi_p][Xi_p]*Theta_4[q*mn*n*sigma_p + q*n*Sigma_p + q*Xi_pp + xi_p];
}
}
C_new[mn*mn*sigma_p + mn*Sigma_p + Xi_p] = sum;
}
}
}
free((void *) Theta_4);
Theta_4 = NULL;
}
void Normalize_T(const int & q, const int & mn, const double * const T_new, double * const T, std::vector<double> & log_beta)
{
double beta = T_new[0];
for(int j=0; j<q*q*mn*mn; j++)
{
if(beta<T_new[j])
{
beta = T_new[j];
}
}
for(int j=0; j<q*q*mn*mn; j++)
{
T[j] = T_new[j]/beta;
}
log_beta.push_back(log(beta));
}
void Normalize_C(const int & q, const int & mn, const double * const C_new, double * const C, std::vector<double> & log_alpha)
{
double alpha = C_new[0];
for(int j=0; j<q*mn*mn; j++)
{
if(alpha<C_new[j])
{
alpha = C_new[j];
}
}
for(int j=0; j<q*mn*mn; j++)
{
C[j] = C_new[j]/alpha;
}
log_alpha.push_back(log(alpha));
}
double Calculate_mag(const int & q, const int & model, const int & n, const MatrixXd & DM)
{
double mag_new = 0;
switch (model)
{
case 0:
for (int a=0; a<n; a++)
{
for (int c=0; c<q; c++)
{
mag_new += 2*(c - 0.5)*DM(q*a + c, q*a + c);
}
}
break;
case 1:
for (int a=0; a<n; a++)
{
for (int c=0; c<q; c++)
{
mag_new += cos(2*pi*c/q)*DM(q*a + c, q*a + c);
}
}
break;
case 2:
for (int a=0; a<n; a++)
{
//mag_new += deltaFunc(c, 0)*DM(q*a + c, q*a + c);
int c = 0;
mag_new += DM(q*a + c, q*a + c);
}
mag_new = (q*mag_new - 1)/(q-1);
break;
}
return mag_new;
}
double Calculate_entropy(const int & q, const int & n, const double * const E)
{
double entropy = 0;
for (int j=0; j<q*n; j++)
{
if ( fabs(E[j]) < 1.E-18 )
{
continue;
}
entropy += - fabs(E[j])*log2(fabs(E[j]));
}
return entropy;
}
double Calculate_U(const int & q, const int & model, const int & n, const double * const C, const double * const T)
{
double *Gamma;
Gamma = (double *)malloc(q*q*n*n*sizeof(double)); //auxiliary array for inner energy
double sum;
for (int x=0; x<q; x++)
{
for (int y=0; y<q; y++)
{
for (int Sigma=0; Sigma<n; Sigma++)
{
for (int Xi_pp=0; Xi_pp<n; Xi_pp++)
{
sum = 0;
for (int Xi=0; Xi<n; Xi++)
{
sum += T[q*n*n*y + q*n*Xi + q*Xi_pp + x]*C[n*n*y + n*Sigma + Xi];
}
Gamma[q*n*n*x + n*n*y + n*Sigma + Xi_pp] = sum;
}
}
}
}
double *Omega;
Omega = (double *)malloc(q*q*n*n*sizeof(double)); //auxiliary array for inner energy
for (int x=0; x<q; x++)
{
for (int y=0; y<q; y++)
{
for (int Sigma=0; Sigma<n; Sigma++)
{
for (int Sigma_pp=0; Sigma_pp<n; Sigma_pp++)
{
sum = 0;
for (int Xi_pp=0; Xi_pp<n; Xi_pp++)
{
sum += C[n*n*x + n*Xi_pp + Sigma_pp]*Gamma[q*n*n*x + n*n*y + n*Sigma + Xi_pp];
}
Omega[q*n*n*x + n*n*y + n*Sigma + Sigma_pp] = sum;
}
}
}
}
free((void *) Gamma);
Gamma = NULL;
double *A;
A = (double *)malloc(q*q*sizeof(double)); //auxiliary array for inner energy
for (int x=0; x<q; x++)
{
for (int y=0; y<q; y++)
{
sum = 0;
for (int Sigma=0; Sigma<n; Sigma++)
{
for (int Sigma_pp=0; Sigma_pp<n; Sigma_pp++)
{
sum += Omega[q*n*n*x + n*n*y + n*Sigma + Sigma_pp]*Omega[q*n*n*x + n*n*y + n*Sigma + Sigma_pp];
}
}
A[q*x + y] = sum;
}
}
free((void *) Omega);
Omega = NULL;
double uZ = 0;
for (int x=0; x<q; x++)
{
for (int y=0; y<q; y++)
{
uZ += A[q*x + y];
}
}
double U_new = 0;
switch (model)
{
case 0:
for (int x=0; x<q; x++)
{
for (int y=0; y<q; y++)
{
double z_x = 2*(x - 0.5);
double z_y = 2*(y - 0.5);
U_new += z_x*z_y*A[q*x + y];
}
}
break;
case 1:
for (int x=0; x<q; x++)
{
for (int y=0; y<q; y++)
{
double t_x = 2*pi*x/q;
double t_y = 2*pi*y/q;
U_new += cos(t_x-t_y)*A[q*x + y];
}
}
break;
case 2:
for (int x=0; x<q; x++)
{
for (int y=0; y<q; y++)
{
U_new += deltaFunc(x, y) * A[q*x + y];
//U_new += deltaFunc(0, y)*A[q*x + y];
//U_new += deltaFunc(x, 0)*A[q*x + y];
}
}
break;
}
free((void *) A);
A = NULL;
U_new *= 2.0;
//U_new *= q;
U_new /= - uZ;
return U_new;
//return ((U_new+1)/(q-1));
}
double Calculate_F(const int & q, const int & i, const int & n, const double & temperature, const double * const C,
const std::vector<double> & log_beta, const std::vector<double> & log_alpha)
{
double fZ = Trace_C4(q, n, C); //fZ - is statistical sum for the system of size (i x i)
long I = i; //type casting - otherwise i*i might be too big (overflow)
double sum_norm_terms = 0;
for (int j=0; j < (i-1)/2; j++)
{
sum_norm_terms += log_alpha[j] + ( (i-1) - 2*(j+1) )*log_beta[j];
}
/* formula for free energy */
double f = - (4*temperature/(I*I))*(log(fZ)/4 + sum_norm_terms);
return f;
}
/*******************************************************************************************************/
double Trace_C4(const int & q, const int & n, const double * const C)
{
double *AF; //auxiliary array
AF = (double *)malloc(q*n*n*sizeof(double));
/* auxiliary array AF initialization */
for (int x=0; x<q; x++)
{
for (int a=0; a<n; a++)
{
for (int c=0; c<n; c++)
{
AF[n*n*x + n*a + c] = 0;
for (int b=0; b<n; b++)
{
AF[n*n*x + n*a + c] += C[n*n*x + n*a + b]*C[n*n*x + n*b + c];
}
}
}
}
/* normalized statistical sum */
double fZ = 0;
for (int c=0; c<n; c++)
{
for (int x=0; x<q; x++)
{
for (int a=0; a<n; a++)
{
fZ += AF[n*n*x + n*a + c]*AF[n*n*x + n*c + a];
}
}
}
free((void *) AF);
AF = NULL;
return fZ;
}
int Increase(const int & q, const int & m, const int & n)
{
int x;
if (q*n <= m)
{
x = q*n;
}
else
{
x = m;
}
return x;
}
//Hamiltonian in Boltzman weight W_B
double H1_Ising(const int &, const double & h, const int & s_1, const int & s_2, const int & s_3, const int & s_4)
{
double z_1 = 2*s_1 - 1;
double z_2 = 2*s_2 - 1;
double z_3 = 2*s_3 - 1;
double z_4 = 2*s_4 - 1;
double h1 = -(z_1*z_2 + z_2*z_3 + z_3*z_4 + z_4*z_1)/2 - h*(z_1 + z_2 + z_3 + z_4)/4;
return h1;
}
//Hamiltonian in transfer matrix T
double H2_Ising(const int &, const double & h, const double & g, const int & s_1, const int & s_2, const int & s_3, const int & s_4)
{
double z_1 = 2*s_1 - 1;
double z_2 = 2*s_2 - 1;
double z_3 = 2*s_3 - 1;
double z_4 = 2*s_4 - 1;
double h2 = -(z_1*z_2 + 2*z_2*z_3 + z_3*z_4 + z_4*z_1)/2 - h*(z_1 + 2*z_2 + 2*z_3 + z_4)/4 - g*(2*z_2 + 2*z_3)/4;
return h2;
}
//Hamiltonian in corner transfer matrix C
double H3_Ising(const int &, const double & h, const double & g, const int & s_1, const int & s_2, const int & s_3, const int & s_4)
{
double z_1 = 2*s_1 - 1;
double z_2 = 2*s_2 - 1;