User contributions for Sw4512

15 February 2015

• 12:0812:08, 15 February 2015 diff hist +3 User:Sw4512cmp →Magnetisation Calculations
• 12:0712:07, 15 February 2015 diff hist +4 User:Sw4512cmp /* Imagine that the system is in the lowest energy configuration. To move to a different state, one of the spins must spontaneously change direction ("flip"). What is the change in energy if this happens (D=3,\ N=1000)? How much entropy does the system...
• 12:0512:05, 15 February 2015 diff hist +10 User:Sw4512cmp →Show that the lowest possible energy for the Ising model is E = -DNJ.

13 February 2015

• 15:1315:13, 13 February 2015 diff hist −471 User:Sw4512cmp /* Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your initution and results from the script ILfinalframe.py to estimate how many cycles each simulation should...
• 15:1015:10, 13 February 2015 diff hist +252 User:Sw4512cmp →Find the temperature at which the maximum in C occurs for each datafile that you were given. Determine T_{C,\infty}. Discuss briefly what you think the major sources of error are in your estimate.
• 15:0615:06, 13 February 2015 diff hist +515 User:Sw4512cmp →Find the temperature at which the maximum in C occurs for each datafile that you were given. Determine T_{C,\infty}. Discuss briefly what you think the major sources of error are in your estimate.
• 14:5814:58, 13 February 2015 diff hist +638 User:Sw4512cmp →Find the temperature at which the maximum in C occurs for each datafile that you were given. Determine T_{C,\infty}. Discuss briefly what you think the major sources of error are in your estimate.
• 14:5214:52, 13 February 2015 diff hist +607 User:Sw4512cmp →Find the temperature at which the maximum in C occurs for each datafile that you were given. Determine T_{C,\infty}. Discuss briefly what you think the major sources of error are in your estimate.
• 14:4914:49, 13 February 2015 diff hist −69 User:Sw4512cmp /* 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 output t...
• 14:4814:48, 13 February 2015 diff hist −107 User:Sw4512cmp /* 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 an exa...
• 14:4714:47, 13 February 2015 diff hist −622 User:Sw4512cmp /* 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 five columns: T, E, E^2, M, M^2, C_V, and you can...
• 14:4514:45, 13 February 2015 diff hist +500 User:Sw4512cmp /* find the temperature at which the maximum in C occurs for each datafile that you were given. Make a text file containing two colums: the lattice side length (2,4,8, etc.), and the temperature at which C is a maximum. This is your estimate of T_C for...
• 14:4114:41, 13 February 2015 diff hist +244 User:Sw4512cmp No edit summary
• 14:3514:35, 13 February 2015 diff hist +1,633 User:Sw4512cmp →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.
• 14:0814:08, 13 February 2015 diff hist +1,707 User:Sw4512cmp /* 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 an exa...
• 13:5313:53, 13 February 2015 diff hist +41 User:Sw4512cmp /* 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 showing th...
• 13:4813:48, 13 February 2015 diff hist −2 User:Sw4512cmp /* find the temperature at which the maximum in C occurs for each datafile that you were given. Make a text file containing two colums: the lattice side length (2,4,8, etc.), and the temperature at which C is a maximum. This is your estimate of T_C for...
• 13:4813:48, 13 February 2015 diff hist 0 User:Sw4512cmp /* find the temperature at which the maximum in C occurs for each datafile that you were given. Make a text file containing two colums: the lattice side length (2,4,8, etc.), and the temperature at which C is a maximum. This is your estimate of T_C for...
• 13:4813:48, 13 February 2015 diff hist +286 User:Sw4512cmp /* find the temperature at which the maximum in C occurs for each datafile that you were given. Make a text file containing two colums: the lattice side length (2,4,8, etc.), and the temperature at which C is a maximum. This is your estimate of T_C for...
• 13:4113:41, 13 February 2015 diff hist −456 User:Sw4512cmp /* 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 {Var}...
• 13:4013:40, 13 February 2015 diff hist +289 User:Sw4512cmp /* 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 {Var}...
• 13:3413:34, 13 February 2015 diff hist +195 User:Sw4512cmp /* Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your initution and results from the script ILfinalframe.py to estimate how many cycles each simulation should...
• 13:3113:31, 13 February 2015 diff hist +226 User:Sw4512cmp /* 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 showing th...
• 13:2913:29, 13 February 2015 diff hist +1 User:Sw4512cmp /* Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your initution and results from the script ILfinalframe.py to estimate how many cycles each simulation should...
• 13:2813:28, 13 February 2015 diff hist −39 User:Sw4512cmp /* Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your initution and results from the script ILfinalframe.py to estimate how many cycles each simulation should...
• 13:2613:26, 13 February 2015 diff hist +111 User:Sw4512cmp /* 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 showing th...
• 13:2413:24, 13 February 2015 diff hist +95 User:Sw4512cmp /* Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your initution and results from the script ILfinalframe.py to estimate how many cycles each simulation should...
• 13:2313:23, 13 February 2015 diff hist −94 User:Sw4512cmp /* 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 showing th...
• 13:2313:23, 13 February 2015 diff hist +1,668 User:Sw4512cmp /* Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your initution and results from the script ILfinalframe.py to estimate how many cycles each simulation should be
• 13:1913:19, 13 February 2015 diff hist +420 User:Sw4512cmp /* 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 showing th...
• 13:1613:16, 13 February 2015 diff hist +619 User:Sw4512cmp /* 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 showing th...
• 12:0212:02, 13 February 2015 diff hist +7 User:Sw4512cmp /* find the temperature at which the maximum in C occurs for each datafile that you were given. Make a text file containing two colums: the lattice side length (2,4,8, etc.), and the temperature at which C is a maximum. This is your estimate of T_C for...
• 12:0212:02, 13 February 2015 diff hist 0 N File:Linearfit sw4512.png No edit summary current
• 11:1611:16, 13 February 2015 diff hist +22 User:Sw4512cmp /* 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 showing th...
• 11:0211:02, 13 February 2015 diff hist +1 User:Sw4512cmp →Magnetisation Calculations

10 February 2015

• 13:2313:23, 10 February 2015 diff hist +234 User:Sw4512cmp /* 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 showing th...
• 13:2213:22, 10 February 2015 diff hist 0 N File:Temprange32x32 sw4512.png No edit summary current
• 13:2213:22, 10 February 2015 diff hist 0 N File:Temprange16x16 sw4512.png No edit summary current
• 13:2013:20, 10 February 2015 diff hist 0 N File:Temprange4x4 sw4512.png No edit summary current
• 13:2013:20, 10 February 2015 diff hist 0 N File:Temprange2x2 sw4512.png No edit summary current
• 11:4811:48, 10 February 2015 diff hist +1 User:Sw4512cmp /* 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 output to P
• 11:4811:48, 10 February 2015 diff hist +777 User:Sw4512cmp /* 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 output t...
• 11:3111:31, 10 February 2015 diff hist +69 User:Sw4512cmp →IsingLattice class
• 11:2311:23, 10 February 2015 diff hist −461 User:Sw4512cmp /* Implement a single cycle of the above algorithm in the montecarlocycle(T) function. This function should return the energy of your lattice and the magnetisation at the end of the cycle. You may assume that the energy returned by your energy() functi...
• 11:2111:21, 10 February 2015 diff hist −2 User:Sw4512cmp →Output of energy() and magnetisation() functions
• 11:2011:20, 10 February 2015 diff hist +19 User:Sw4512cmp →Output of energy() and magnetisation() functions
• 11:1911:19, 10 February 2015 diff hist +29 User:Sw4512cmp →Magnetisation Calculations
• 11:1811:18, 10 February 2015 diff hist +93 User:Sw4512cmp /* Imagine that the system is in the lowest energy configuration. To move to a different state, one of the spins must spontaneously change direction ("flip"). What is the change in energy if this happens (D=3,\ N=1000)? How much entropy does the system...

9 February 2015

• 22:4822:48, 9 February 2015 diff hist +12 User:Sw4512cmp /* 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 animati...
• 22:4622:46, 9 February 2015 diff hist +74 User:Sw4512cmp /* 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 output t...