PHYSICS
11 THE RANDOM WALKER 11 1 (PSEUDO)RANDOM NUMBERS 11 2 USING PSEUDORANDOM NUMBER GENERATORS 11 3 THE MIXMAX RANDOM NUMBER GENERATOR 11 4 RANDOM WALKS 11 5 PROBLEMS 12 MONTE CARLO SIMULATIONS 12 1 STATISTICAL PHYSICS 12 2 ENTROPY 12 3 FLUCTUATIONS 12 4 CORRELATION FUNCTIONS 12 5 SAMPLING 12 5 1 SIMPLE SAMPLING 12 5 2 IMPORTANCE SAMPLING 12 6 MARKOV PROCESSES 12 7 DETAILED BALANCE CONDITION 12 8 PROBLEMS 13 SIMULATION OF THE D = 2 ISING MODEL 13 1 THE ISING MODEL 13 2 METROPOLIS 13 3 IMPLEMENTATION 13 3 1 THE PROGRAM 13 3 2 TOWARDS A CONVENIENT USER INTERFACE 13 4 THERMALIZATION 13 5 AUTOCORRELATIONS 13 6 STATISTICAL ERRORS 13 6 1 ERRORS OF INDEPENDENT MEASUREMENTS 13 6 2 JACKKNIFE 13 6 3 BOOTSTRAP 13 7 APPENDIX: AUTOCORRELATION FUNCTION 13 8 APPENDIX: ERROR ANALYSIS 13 8 1 THE JACKKNIFE METHOD 13 8 2 THE BOOTSTRAP METHOD 13 8 3 COMPARING THE METHODS 13 9 PROBLEMS 14 CRITICAL EXPONENTS 14 1 CRITICAL SLOWING DOWN 14 2 WOL?CLUSTER ALGORITHM 14 3 IMPLEMENTATION 14 3 1 THE PROGRAM 14 4 PRODUCTION 14 5 DATA ANALYSIS 14 6 AUTOCORRELATION TIMES 14 7 TEMPERATURE SCALING 14 8 FINITE SIZE SCALING 14 9 CALCULATION OF ?C 14 10STUDYING SCALING WITH COLLAPSE 14 11BINDER CUMULANT 14 12APPENDIX: SCALING 14 12 1BINDER CUMULANT 14 12 2SCALING 14 12 3FINITE SIZE SCALING 14 13APPENDIX: CRITICAL EXPONENTS 14 13 1DE?NITIONS 14 13 2HYPERSCALING RELATIONS 14 14PROBLEMS