Finitetemp exercises.

content/finitetemp/SimpleCubic/inpsd.dat

@@ -0,0 +1,31 @@
+simid simpcube
+ncell     10        10       10                 System size            
+BC        P         P         P                 Boundary conditions (0=vacuum, P=periodic)
+cell      1.00000   0.00000   0.00000         
+          0.00000   1.00000   0.00000
+          0.00000   0.00000   1.00000
+Sym       1                                     Symmetry of lattice (0 for no, 1 for cubic, 2 for 2d cubic, 3 for hexagonal)
+do_prnstruct 1
+
+posfile      ./posfile
+momfile      ./momfile
+exchange     ./jfile
+
+Initmag     3                                   Initial config of moments (1=random, 2=cone, 3=spec., 4=file)
+
+ip_mode     N
+ip_mcanneal 1
+            5000  300.0 1.00e-16 0.95
+
+mode        S
+Temp        300.00          K                    Temperature of the system
+hfield      0.00000   0.00000   0.00000          Static H field
+
+damping     0.01                                 Damping parameter (gamma)
+nstep       10000                                Number of time-steps
+timestep    1.000e-16       s                    The time step-size for the SDE-solver
+
+plotenergy  1                                    Sample energies
+do_avrg     Y                                    Measure averages
+do_cumu     Y                                    Sample cumulative averages
+do_spintemp Y                                    Measure spin temperature

content/finitetemp/SimpleCubic/jfile

@@ -0,0 +1,2 @@
+1 1  1.0       0.0       0.0       0.80000000000000
+1 1  1.0       1.0       0.0       0.50000000000000

content/finitetemp/SimpleCubic/momfile

@@ -0,0 +1 @@
+1 1 1.00 0.0 0.0 1.0 

content/finitetemp/SimpleCubic/posfile

@@ -0,0 +1 @@
+1 1   0.000000  0.000000  0.000000

content/finitetemp/SingleSpin/inpsd.dat

@@ -0,0 +1,35 @@
+simid     SingleSP 
+ncell     1         1         1                 System size
+BC        0         0         0                 Boundary conditions (0=vacuum,P=periodic)
+cell      0.00000   0.00000   0.00000
+          0.00000   0.00000   0.00000
+          0.00000   0.00000   0.00000
+Sym       0                                     Symmetry of lattice (0 for no, 1 for cubic, 2 for 2d cubic, 3 for hexagonal)
+do_prnstruct 2                                  Print lattice structure (0=no, 1=yes, 2=coordinates only)
+
+posfile    ./posfile
+exchange   ./jfile
+momfile    ./momfile
+anisotropy ./kfile
+
+Mensemble 1                                     Number of samples in ensemble averaging
+Initmag   3                                     (1=random, 2=cone, 3=spec., 4=file)
+
+ip_mode   N                                     Initial phase parameters
+
+mode      S                                     S=SD, M=MC
+temp      5.00                                 Measurement phase parameters
+damping   0.50000                               --
+Nstep     150000                                  --
+timestep  1.000e-15                             --
+
+do_avrg   Y                                     Measure averages
+avrg_step 100 
+
+do_tottraj Y                                    Measure moments
+tottraj_step       10000
+tottraj_buff       10                           time step, buffer size
+
+do_cumu Y
+
+real_time_measure Y

content/finitetemp/SingleSpin/jfile

@@ -0,0 +1 @@
+ 1 1    0.0    0.0    1.0    0.0000

content/finitetemp/SingleSpin/kfile

@@ -0,0 +1 @@
+ 1 1   -0.100   0.0    0.0   0.0   1.0   0.0

content/finitetemp/SingleSpin/momfile

@@ -0,0 +1 @@
+1 1 1.00000   0.00000  0.0000  1.0000

content/finitetemp/SingleSpin/posfile

@@ -0,0 +1 @@
+1   1   0.0 0.0 0.0                    

content/finitetemp/SquareLattice/Base/inpsd.dat

@@ -0,0 +1,28 @@
+simid  scHeis64 
+ncell     64 64 1
+BC        P         P         0                 Boundary conditions (0=vacuum,P=periodic)
+cell      1.00000   0.00000   0.00000
+          0.00000   1.00000   0.00000
+          0.00000   0.00000   1.00000
+Sym       1                                     Symmetry of lattice (0 for no, 1 for cubic, 2 for 2d cubic, 3 for hexagonal)
+
+aunits Y
+posfile    ./posfile
+exchange   ./jfile
+momfile    ./momfile
+do_prnstruct 1
+
+Mensemble 1
+Initmag   3                                     (1=random, 2=cone, 3=spec., 4=file)
+
+ip_mode   M                                     Initial phase parameters
+ip_temp   TEMP                                  --
+ip_mcNstep     5000                            --
+
+mode      M                                     S=SD, M=MC
+temp      TEMP                                  Measurement phase parameters
+mcNstep   5000                                --
+
+do_avrg   Y                                     Measure averages
+plotenergy 1
+do_cumu Y

content/finitetemp/SquareLattice/Base/jfile

@@ -0,0 +1 @@
+ 1 1    1.0    0.0    0.0    0.5000

content/finitetemp/SquareLattice/Base/momfile

@@ -0,0 +1 @@
+1 1 1.00000 0.0 0.0 1.0

content/finitetemp/SquareLattice/Base/posfile

@@ -0,0 +1 @@
+1   1   0.0 0.0 0.0                    

content/finitetemp/SquareLattice/printM.sh

@@ -0,0 +1,13 @@
+#! /bin/csh -f 
+foreach Temp (0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0)
+          echo $Temp | sed ' s/K//' > tmp
+          cat tmp >> Tlist
+          cat T$Temp/cumulants.scHeis64.out | tail -1 | awk '{print $2}' > tmp1
+          cat T$Temp/cumulants.scHeis64.out | tail -1 | awk '{print $5}' > tmp2
+          cat tmp1 >> Mlist
+          cat tmp2 >> Ulist
+end
+
+paste Tlist Mlist Ulist > magnetization.dat
+rm Tlist Mlist Ulist tmp tmp1 tmp2
+exit

content/finitetemp/SquareLattice/runme.sh

@@ -0,0 +1,12 @@
+#!/bin/bash
+
+for Temp in 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
+do
+    mkdir T$Temp/
+    echo "Temp: " $Temp
+    cp Base/* T$Temp/
+    cd T$Temp/
+    gsed -i "s/TEMP/$Temp/g" inpsd.dat
+    ${SD_BINARY} > out.log
+    cd ..
+done

content/finitetemp/SquareLattice/sc_64_ALPS.dat

@@ -0,0 +1,42 @@
+#       Temperature (J)   Magnetization
+         0.01000000        0.99162215 
+         0.06000000        0.95483038 
+         0.11000000        0.92026908 
+         0.16000000        0.88392499 
+         0.21000000        0.83767839 
+         0.26000000        0.80447273 
+         0.31000000        0.75743914 
+         0.36000000        0.71563720 
+         0.41000000        0.66379796 
+         0.46000000        0.60234222 
+         0.51000000        0.55313209 
+         0.56000000        0.47708797 
+         0.61000000        0.34753675 
+         0.66000000        0.21652653 
+         0.71000000        0.12810921 
+         0.76000000        0.09693399 
+         0.81000000        0.07360353 
+         0.86000000        0.06022234 
+         0.91000000        0.05290496 
+         0.96000000        0.04736220 
+         1.01000000        0.04230193 
+         1.06000000        0.03953494 
+         1.11000000        0.03636440 
+         1.16000000        0.03424181 
+         1.21000000        0.03237245 
+         1.26000000        0.03086418 
+         1.31000000        0.02957311 
+         1.36000000        0.02842018 
+         1.41000000        0.02759275 
+         1.46000000        0.02657334 
+         1.51000000        0.02610488 
+         1.56000000        0.02525342 
+         1.61000000        0.02479467 
+         1.66000000        0.02425726 
+         1.71000000        0.02366309 
+         1.76000000        0.02337222 
+         1.81000000        0.02274532 
+         1.86000000        0.02252159 
+         1.91000000        0.02217737 
+         1.96000000        0.02185710 
+         2.01000000        0.02166938 

content/finitetemp/finitetemp.rst

@@ -1,2 +1,92 @@
 Finite temperatures
 ===================
+
+
+Statistics
+----------
+In this exercise we will investigate how statistics affect simulated measurables.
+
+A single spin with an uniaxial anisotropy has a bi-stable, Ising like, magnetic state. At finite temperatures the stability of the magnetic state is not finite
+but follows an exponential (Arrhenius) relaxation behaviour. As seen in the lecture, ensemble averaging can be crucial for the analysis of such systems.
+
+ * Investigate the amount of statistics that is needed to say something relevant about the life time of the magnetic state of the system. 
+
+ * Does the need of statistics change with system parameters? (temperature, anisotropy, external field)
+
+ * Extra: Can you fit the relaxation behaviour to an `Arrhenius function <https://en.wikipedia.org/wiki/Arrhenius_equation>`_? 
+
+You can do a similar analysis for a finite 1d-chain by either modifying the single spin example, or 
+starting from the `SimpleSystems/HeisChain <https://github.com/UppASD/UppASD/tree/master/examples/SimpleSystems/HeisChain>`_ example.
+
+ * Is there a difference by performing ensemble averaging compared to just increasing the system size?
+
+ * Does the exchange interaction magnitude affect the stability of the spin chains?
+
+An accessible article for those interested in spin chains and statistics can be found here: `A. Vindigni Inorganica Chimica Acta, 361 3731 (2008) <https://www.sciencedirect.com/science/article/abs/pii/S0020169308001588>`_.
+
+
+
+Thermalization
+--------------
+In this exercise the thermalization rates in spin simulations will be investigated. 
+
+As mentioned in the lecture, thermalising the system before performing measurements is crucial for ensuring relevant results. 
+Here we will investigate this for a simple cubic model system.
+
+The initial ``inpsd.dat`` file looks as follows 
+
+.. literalinclude:: SimpleCubic/inpsd.dat
+
+and the almost trivial ``posfile`` and ``momfile`` are written as 
+
+.. literalinclude:: SimpleCubic/posfile
+.. literalinclude:: SimpleCubic/momfile
+
+The ``jfile``, that will be changed during the exercise initially can look like
+
+.. literalinclude:: SimpleCubic/jfile
+
+i.e. including nearest and next-nearest neighbours on the cubic lattice. Notice that since ``sym 1`` is given in ``inpsd.dat``, the ``jfile`` can be kept to a minimum of two lines.
+
+ * Starting with the inputs as defined above, vary the simulation method and damping (where applicable) to investigate the thermalization rate of the system.
+
+ * Is the thermalization faster when going from low to high temperatures or vice versa? Anything particular happening around Tc?
+
+ * Change the sign of the next-nearest neighbour and redo the study. Is the magnetization a good measurable for determining the thermalization now?
+
+Phase diagrams
+--------------
+Obtaining the M vs T relationship is probably the most common use case for Monte Carlo simulations on spin systems. 
+In this exercise you can compare the MC functionalities of UppASD with a the ALPS package. 
+
+The system in question is here the 2d square lattice with NN exchange couplings. 
+To compare with other model implementations this example uses the ``aunits Y`` flag which sets the temperature unit to the exchange strength ``J`` instead of Kelvin.
+
+The ``inpsd.dat`` will here look as follows (to start with). Note the **TEMP** entries for initial and measurement temperatures.
+
+.. literalinclude:: SquareLattice/Base/inpsd.dat
+
+and the ``posfile`` and ``momfile``, and ``jfile`` files looks as 
+
+.. literalinclude:: SquareLattice/Base/posfile
+.. literalinclude:: SquareLattice/Base/momfile
+.. literalinclude:: SquareLattice/Base/jfile
+
+Again, note that with ``aunits Y`` the exchange interaction in ``jfile`` is not defined in ``mRy`` but in the dimensionless energy scale of ``J`` (not Joule either).
+
+In order to obtain the full M(T) curve, several simulations are needed at consecutive temperatures. 
+This is preferably scripted, like in this example where we use a simple ``bash`` script ``runme.sh``
+
+.. literalinclude:: SquareLattice/runme.sh
+
+Here you either need to replace the ``${SD_BINARY}`` expression, or export the location of your UppASD binary as the environment variable with the same name.
+
+ * Run the script and plot the resulting M(T) curve. 
+
+ * Compare with the reference data in the :download:`sc_64_ALPS.dat <SquareLattice/sc_64_ALPS.dat>` file
+
+ * Are the simulation parameters "good enough" or are more thermalization/sampling steps needed to obtain an accurate M(T) curve?
+
+
+Minimization
+------------