Computational Physics

10.3 Importance sampling through Markov chains 303 In the next subsections we shall work out the canonical ensemble MC method in ...

304 The Monte Carlo method 10.3.1 Monte Carlo for the Ising model The Ising model was discussed in Chapter 7. Here we consider t ...

10.3 Importance sampling through Markov chains 305 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 1 2 3 4 5 6 7 Specific heat
Figure 10.1 ...

306 The Monte Carlo method separating the metastable from the stable phase. This can also be checked: below the critical tempera ...

10.3 Importance sampling through Markov chains 307 0 20 40 60 80 100 120 Magnetisation 10 MCS^3 –1 –0.8 –0.6 –0.4 –0.2 0 0.2 0.4 ...

308 The Monte Carlo method that the acceptance probability for each such new configuration is proportional to exp[−βE(X→X′)]. T ...

10.3 Importance sampling through Markov chains 309 the trial configuration is accepted or rejected as usual, with an acceptance ...

310 The Monte Carlo method programming exercise Code the Metropolis method for argon, and compare the results with those of the ...

10.4 Other ensembles 311 The(NPT)ensemble average of a physical quantityAdepending on the positions R=r 1 ,...,rNis given as 〈A〉 ...

312 The Monte Carlo method The calculation of the potential energy difference associated with a volume change is rather demandin ...

10.4 Other ensembles 313 and annihilation of particles should be possible. Let us write down the probabil- ity distribution of c ...

314 The Monte Carlo method This form of grand canonical Monte Carlo was presented by Norman and Filinov [23]. Other approaches t ...

10.4 Other ensembles 315 subsystem (V 2 ) minus the interactions it felt in its previous subsystem (V 1 ). These moves are actua ...

316 The Monte Carlo method It is not necessary to separate the two subvolumes by a movable piston in order to arrive at equal pr ...

10.5 Estimation of free energy and chemical potential 317 method for doing this is thermodynamic integration, described inSectio ...

318 The Monte Carlo method The quotients in this expression are canonical ensemble averages corresponding to Z 0 Z 1 = 〈M[β(U 0 ...

10.6 Further applications and Monte Carlo methods 319 [36]. The method works well, although problems arise for high densities. I ...

320 The Monte Carlo method represent segments of the polymer; the segments in turn represent groups of atoms. These atomic group ...

10.6 Further applications and Monte Carlo methods 321 Another approach is inspired by a particular type of motion of polymers: r ...

322 The Monte Carlo method Calculating the actual probability for a particular configuration to occur, we find P= ∏N l= 3 wj(l) ...