Computational Physics - Department of Physics

13.4 Phase Transitions and Critical Phenomena 429 limit ourselves to list Onsager’s result 〈M(T)/N〉= [ 1 − ( 1 −tanh^2 (βJ))^4 1 ...

430 13 Monte Carlo Methods in Statistical Physics out is renormalization group theory [75–81]. Table 13.5 lists some typical sys ...

13.4 Phase Transitions and Critical Phenomena 431 marked by one or more thermodynamical variables which vanish above a critical ...

432 13 Monte Carlo Methods in Statistical Physics and the susceptibility χ(T)∼|TC−T|−γ, withα= 0 andγ=− 7 / 4. Another important ...

13.4 Phase Transitions and Critical Phenomena 433 interaction between two spins at sitesiandj, respectively, by adding and subtr ...

434 13 Monte Carlo Methods in Statistical Physics and if we assume thatmis real we have two solutions m= 0 , or m^2 = b 2 c ( − ...

13.5 The Metropolis Algorithm and the Two-dimensional Ising Model 435 choice for solving the Ising model is the approach propose ...

436 13 Monte Carlo Methods in Statistical Physics Actually, there are only five possible values. To see this, select first a ran ...

13.5 The Metropolis Algorithm and the Two-dimensional Ising Model 437 voidinitialize(int,double,int,double&,double&); // ...

438 13 Monte Carlo Methods in Statistical Physics eβ ∆E. This is easily done in the Ising model since we can exploit the fact th ...

13.5 The Metropolis Algorithm and the Two-dimensional Ising Model 439 magnetisation. The new values are used to update the avera ...

440 13 Monte Carlo Methods in Statistical Physics for(inty =0; y < n_spins; y++){ for(intx= 0; x < n_spins; x++){ E -= (do ...

13.5 The Metropolis Algorithm and the Two-dimensional Ising Model 441 include include include include include"lib.h" using names ...

442 13 Monte Carlo Methods in Statistical Physics // Allocate memory for spin matrix spin_matrix = (int) matrix(n_spins, n_spins ...

13.6 Selected Results for the Ising Model 443 " 100 × 100 " " 80 × 80 " " 40 × 40 " " 10 × 10 " kBT E/ J 1.6 1.8 2 2.2 2.4 2.6 0 ...

444 13 Monte Carlo Methods in Statistical Physics The reason we choose to plot the average absolute value instead of the net mag ...

13.7 Correlation Functions and Further Analysis of the Ising Model 445 " 100 × 100 " " 80 × 80 " " 40 × 40 " " 10 × 10 " kBT χ 2 ...

446 13 Monte Carlo Methods in Statistical Physics ter 11. There we considered a box divided into two equal halves separated by a ...

13.7 Correlation Functions and Further Analysis of the Ising Model 447 kBT/J= 2. 4 kBT/J= 1. 5 t |M | 0 100 200 300 400 500 600 ...

448 13 Monte Carlo Methods in Statistical Physics Cooling the system further we observe clusters pervading larger areas of the l ...