Advanced_StatPhys

Preliminaries

Before getting started with your simulation, please create the directories you need to save and read your data as follows:

project
│   README.md
|   figs
│   src
|   ...
└───data
      └───avg
      |     └───mag
      |     |    └───L128
      |     |    └───L64
      |     |    └───L32
      |     |    └───L16
      |     |    └───L8
      |     └───sus
      |          └───L128
      |          └───L64
      |          └───L32
      |          └───L16
      |          └───L8
      └───mag
      |    └───L128
      |    └───L64
      |    └───L32
      |    └───L16
      |    └───L8
      └───sus
           └───L128
           └───L64
           └───L32
           └───L16
           └───L8

Introduction

This project is made up of mainly two parts: Simulating Ising model on 2D SQL & Finite-size scaling analysis.

The source code of the Ising model is made with C, and you can use it with the python3 wrapper, "run_single.py". With "run_single.py", you can measure the magnetization (order parameter), susceptibility and calculate the average values and errors of them. For extensive Monte Carlo simulations at $T_c \approx 2.269185$, you can use "run_at_TC.py"

The basic command line usage:

python3 run_single.py

python3 run_at_TC.py

Modifying source codes

If you want to modify the source codes, you need to change the files in the directory "src".

ising2d.c

• N_ITER : the number of repeated simulations
• THERMALIZATION_T: the time we are waiting to reach the steady state
• MEASURE_T: the time we are measuring the magnetization after we reach the steady state

You can compile your new program as follows: gcc -O3 -o ising2d.out ising2d.c -lm

bootstrap4sus.c

• N_measure : the number measurements you will make
• N_sample: the size of sampled data when you measure once

You can compile your new program as follows: gcc -O3 -o bs.out bootstrap4sus.c -lm

make_avg.c

• Here, you have nothing to modify. This is just to calculate the mean and standard deviation values.

Anyway, you can compile your new program as follows: gcc -O3 -o avg.out make_avg.c -lm

Finite-size scaling analysis

You can measure the exponents and collapse the data in "FSS_analysis.ipynb". All directories are prepared, and you only need to press enters.

Basic workflow

1. Carry out measurements on magnetizations with "run_single.py" and "run_at_TC.py"
2. Carry out measurements on susceptibility with "run_single.py"
3. Calculate mean and error values of magnetization and susceptibility with "run_single.py".
4. Work on your finite-size scaling analysis with "FSS_analysis.ipynb".

Good luck for your further projects :)