User contributions for Hhc16

11:4711:47, 21 November 2018 diff hist +81 Rep:Simulations of a 2D Ising Model (hhc16) →Conclusion
11:4511:45, 21 November 2018 diff hist +194 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: find the temperature at which the maximum in C occurs for each datafile that you were given. Make a text file containing two columns: the lattice side length (2,4,8, etc.), and the temperature at which C is a maximum. This is your estimate of...
11:4311:43, 21 November 2018 diff hist +10 Rep:Simulations of a 2D Ising Model (hhc16) →Conclusion
11:4311:43, 21 November 2018 diff hist +192 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section. You may need to do some research to recall the connection between the variance of a variable, \mathrm{V...
11:4111:41, 21 November 2018 diff hist +195 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: If T , do you expect a spontaneous magnetisation (i.e. do you expect \left\langle M\right\rangle \neq 0)? When the state of the simulation appears to stop changing (when you have reached an equilibrium state), use the controls to export the ou...
11:3911:39, 21 November 2018 diff hist +75 Rep:Simulations of a 2D Ising Model (hhc16) →Incorporating Monte Carlo Method
11:3811:38, 21 November 2018 diff hist +62 Rep:Simulations of a 2D Ising Model (hhc16) →Incorporating Monte Carlo Method
11:3411:34, 21 November 2018 diff hist +61 Rep:Simulations of a 2D Ising Model (hhc16) →TASK: Show that the lowest possible energy for the Ising model is E\ =\ -DNJ, where D is the number of dimensions and N is the total number of spins. What is the multiplicity of this state? Calculate its entropy.
11:3211:32, 21 November 2018 diff hist +84 Rep:Simulations of a 2D Ising Model (hhc16) →The Model
11:3211:32, 21 November 2018 diff hist 0 Rep:Simulations of a 2D Ising Model (hhc16) →Introduction
11:3011:30, 21 November 2018 diff hist +141 Rep:Simulations of a 2D Ising Model (hhc16) →Introduction
11:2711:27, 21 November 2018 diff hist +878 Rep:Simulations of a 2D Ising Model (hhc16) →Conclusion
11:0611:06, 21 November 2018 diff hist 0 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section. You may need to do some research to recall the connection between the variance of a variable, \mathrm{V...
11:0511:05, 21 November 2018 diff hist 0 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section. You may need to do some research to recall the connection between the variance of a variable, \mathrm{V...
11:0411:04, 21 November 2018 diff hist +31 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section. You may need to do some research to recall the connection between the variance of a variable, \mathrm{V...
11:0311:03, 21 November 2018 diff hist +77 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section. You may need to do some research to recall the connection between the variance of a variable, \mathrm{V...
11:0111:01, 21 November 2018 diff hist +41 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your intuition and results from the script ILfinalframe.py to estimate how many cycles each simulation...
10:5910:59, 21 November 2018 diff hist −18 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section. You may need to do some research to recall the connection between the variance of a variable, \mathrm{V...
10:5810:58, 21 November 2018 diff hist +55 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your intuition and results from the script ILfinalframe.py to estimate how many cycles each simulation...
10:5410:54, 21 November 2018 diff hist +36 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Repeat the final task of the previous section for the following lattice sizes: 2x2, 4x4, 8x8, 16x16, 32x32. Make sure that you name each datafile that your produce after the corresponding lattice size! Write a Python script to make a plot show...
10:4610:46, 21 November 2018 diff hist +316 Rep:Simulations of a 2D Ising Model (hhc16) →The Effect of System Size
10:3810:38, 21 November 2018 diff hist +111 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your intuition and results from the script ILfinalframe.py to estimate how many cycles each simulation...
10:2810:28, 21 November 2018 diff hist +22 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your intuition and results from the script ILfinalframe.py to estimate how many cycles each simulation...
10:2710:27, 21 November 2018 diff hist +110 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your intuition and results from the script ILfinalframe.py to estimate how many cycles each simulation...
10:1210:12, 21 November 2018 diff hist +30 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: The script ILfinalframe.py runs for a given number of cycles at a given temperature, then plots a depiction of the final lattice state as well as graphs of the energy and magnetisation as a function of cycle number. This is much quicker than a...
09:0409:04, 21 November 2018 diff hist +335 Rep:Simulations of a 2D Ising Model (hhc16) →Conclusion
03:4303:43, 21 November 2018 diff hist +15 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: find the temperature at which the maximum in C occurs for each datafile that you were given. Make a text file containing two columns: the lattice side length (2,4,8, etc.), and the temperature at which C is a maximum. This is your estimate of...
03:4203:42, 21 November 2018 diff hist −12 Rep:Simulations of a 2D Ising Model (hhc16) →TASK: Modify your script from the previous section. You should still plot the whole temperature range, but fit the polynomial only to the peak of the heat capacity! You should find it easier to get a good fit when restricted to this region.
03:4103:41, 21 November 2018 diff hist +15 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: write a script to read the data from a particular file, and plot C vs T, as well as a fitted polynomial. Try changing the degree of the polynomial to improve the fit — in general, it might be difficult to get a good fit! Attach a PNG of...
03:4003:40, 21 November 2018 diff hist +380 Rep:Simulations of a 2D Ising Model (hhc16) →Conclusion
03:3603:36, 21 November 2018 diff hist −97 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: A C++ program has been used to run some much longer simulations than would be possible on the college computers in Python. You can view its source code here if you are interested. Each file contains six columns: T, E, E^2, M, M^2, C (the final...
03:3503:35, 21 November 2018 diff hist +38 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: A C++ program has been used to run some much longer simulations than would be possible on the college computers in Python. You can view its source code here if you are interested. Each file contains six columns: T, E, E^2, M, M^2, C (the final...
03:3403:34, 21 November 2018 diff hist +134 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section. You may need to do some research to recall the connection between the variance of a variable, \mathrm{V...
03:3103:31, 21 November 2018 diff hist −130 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section. You may need to do some research to recall the connection between the variance of a variable, \mathrm{V...
03:3003:30, 21 November 2018 diff hist 0 Rep:Simulations of a 2D Ising Model (hhc16) →TASK: By definition, C = \frac{\partial \left\langle E\right\rangle}{\partial T}. From this, show that C = \frac{\mathrm{Var}[E]}{k_B T^2}. Where \mathrm{Var}[E] is the variance in E.
03:3003:30, 21 November 2018 diff hist +1 Rep:Simulations of a 2D Ising Model (hhc16) →The Effect of System Size
03:2903:29, 21 November 2018 diff hist 0 Rep:Simulations of a 2D Ising Model (hhc16) →Running Over a Range of Temperatures
03:2803:28, 21 November 2018 diff hist 0 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: The script ILfinalframe.py runs for a given number of cycles at a given temperature, then plots a depiction of the final lattice state as well as graphs of the energy and magnetisation as a function of cycle number. This is much quicker than a...
03:2803:28, 21 November 2018 diff hist −109 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section. You may need to do some research to recall the connection between the variance of a variable, \mathrm{V...
03:1703:17, 21 November 2018 diff hist +17 Rep:Simulations of a 2D Ising Model (hhc16) →TASK: By definition, C = \frac{\partial \left\langle E\right\rangle}{\partial T}. From this, show that C = \frac{\mathrm{Var}[E]}{k_B T^2}. Where \mathrm{Var}[E] is the variance in E.
03:1703:17, 21 November 2018 diff hist +1 Rep:Simulations of a 2D Ising Model (hhc16) →The Effect of System Size
03:1703:17, 21 November 2018 diff hist +16 Rep:Simulations of a 2D Ising Model (hhc16) →The Effect of System Size
03:1603:16, 21 November 2018 diff hist +259 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Repeat the final task of the previous section for the following lattice sizes: 2x2, 4x4, 8x8, 16x16, 32x32. Make sure that you name each datafile that your produce after the corresponding lattice size! Write a Python script to make a plot show...
03:0103:01, 21 November 2018 diff hist +16 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your intuition and results from the script ILfinalframe.py to estimate how many cycles each simulation...
03:0003:00, 21 November 2018 diff hist +21 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: The script ILfinalframe.py runs for a given number of cycles at a given temperature, then plots a depiction of the final lattice state as well as graphs of the energy and magnetisation as a function of cycle number. This is much quicker than a...
02:5702:57, 21 November 2018 diff hist +4 Rep:Simulations of a 2D Ising Model (hhc16) →Correcting the Averaging Code
02:5502:55, 21 November 2018 diff hist +12 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Use the script ILtimetrial.py to record how long your new version of IsingLattice.py takes to perform 2000 Monte Carlo steps. This will vary, depending on what else the computer happens to be doing, so perform repeats and report the error in y...
02:5302:53, 21 November 2018 diff hist +12 Rep:Simulations of a 2D Ising Model (hhc16) →Modifying IsingLattice.py
02:4902:49, 21 November 2018 diff hist +2 Rep:Simulations of a 2D Ising Model (hhc16) →Incorporating Monte Carlo Method
02:4902:49, 21 November 2018 diff hist +14 Rep:Simulations of a 2D Ising Model (hhc16) →Incorporating Monte Carlo Method

21 November 2018