Appendix 3: Contents of the Disk

The computer disk which accompanied the thesis as submitted to the examiners in July 2000 contained the following files:

  1. The ISM.EXE simulation program, Version 1.93 (in directory EXE), which is described in detail in Section 2.1.
  2. NOTEPAD.EXE (in directory EXE), a text editor which is invoked by ISM upon completion of the simulation to display results written to the output file.
  3. The following input files (in directory EXE):
  4. (i) I2TRI20.IN  The input file specifies simulations using an Ising model of size 20x20 on a triangular lattice, for two temperatures, T = 3.5 and T = 3.8, using Swendsen-Wang dynamics and 1000 samples. Due to the small lattice size and the small number of samples, the simulations require less than three minutes each to run. (All run times given in this Appendix were obtained by running the simulation software on a 330 MHz PC.) To run the simulation enter ISM I2TRI20.IN at the command line prompt. (ISM.EXE may be run from the disk, since there is no file I/O until the program writes its results to the output file after about six minutes.) The output file I2TRI20.OUT may then be opened using the Excel spreadsheet and the magnetization data may be plotted to reproduce the plot for lattice size 20 and the two temperatures as shown in Figure 3.2.1 in Section 3.2.

    (ii) I3CU8.IN  The input file specifies some of the simulations used to obtain the critical temperature of the pure Ising model on a cubic lattice, using a lattice of size 8x8x8, Wolff dynamics and 1000 samples. The Binder cumulant is computed for six temperatures in the range 4.49 to 4.54 (data is written to the output file once for each temperature). These five runs take a total of about twelve minutes. The output file, I3CU8.OUT, may be opened within Excel, and the Binder cumulant plotted against temperature, to reproduce the plot for lattice size 8 given in Figure 3.4.5 in Section 3.4.

    (iii) I3CUW10.IN  The input file specifies some of the simulations used to obtain the critical temperature of the cubic Ising model with site dilution of 0.8, using a lattice of size 10x10x10, Wolff dynamics and 2000 samples. The Binder cumulant is computed for six temperatures in the range 3.485 to 3.510. These five simulations take a total of about 32 minutes. The output file, I3CUW10.OUT, may be opened within Excel and the Binder cumulant plotted against temperature, to reproduce the plot for lattice size 10 given in Figure 4.2.1 in Section 4.2.

    (iv) L200.IN  The input file specifies the simulation used to obtain the data for Figure 5.5.1 (a plot of absolute magnetization against time for the 3-state Potts model using a square lattice of size 200x200 at temperature = 99% of the critical temperature). A simulation using 8000 samples requires about 36 hours of computing time (although a similar plot may be obtained using only 2000 samples).

  5. The FIT.EXE program (in directory FIT), described in Appendix 4, "The FIT Programs".
  6. The following input files (in directory FIT):
  7. (i) M1BIS.TXT and M2BIS.TXT  These two files contain the data in Table 5.2.2 in Section 5.2. Run the FIT program (FIT M1BIS.TXT) to obtain the least-squares fit given in that section.

    (ii) IS-MAG.TXT  The file of log-log magnetization values plotted in Figure 6.2.1 which, when acted upon by the FIT program, produces the least-squares fit given in Section 6.2(i).

    (iii) DBAUTO.TXT  The file of log-log autocorrelation values plotted in Figure 6.4.2 which, when acted upon by the FIT program, produces the least-squares fit given in Section 6.4.

  8. The 4STPFIT.EXE program (in directory 4STPFIT), described in Appendix 4, "The FIT Programs". Also the files BT.OUT and DB.OUT (see Appendix 4(iii)).

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