TY - JOUR

T1 - Monte Carlo study of the pure and dilute Baxter-Wu model

AU - Schreiber, Nir

AU - Adler, Joan

PY - 2005/8/19

Y1 - 2005/8/19

N2 - We studied the pure and dilute Baxter-Wu (BW) models using the Wang-Landau (WL) sampling method to calculate the density-of-states (DOS). We first used the exact result for the DOS of the Ising model to test our code. Then we calculated the DOS of the dilute Ising model to obtain a phase diagram, in good agreement with previous studies. We calculated the energy distribution, together with its first, second and fourth moments, to give the specific heat and the energy fourth order cumulant, better known as the Binder parameter, for the pure BW model. For small samples, the energy distribution displayed a doubly peaked shape, and finite size scaling analysis showed the expected reciprocal scaling of the positions of the peaks with L. The energy distribution yielded the expected BW α ≤ 2/3 critical exponent for the specific heat. The Binder parameter minimum appeared to scale with lattice size L with an exponent θB equal to the specific heat exponent. Its location (temperature) showed a large correction-to-scaling term θ1 ≤ 0.248 ± 0.025. For the dilute BW model we found a clear crossover to a single peak in the energy distribution even for small sizes and the expected α ≤ 0 was recovered.

AB - We studied the pure and dilute Baxter-Wu (BW) models using the Wang-Landau (WL) sampling method to calculate the density-of-states (DOS). We first used the exact result for the DOS of the Ising model to test our code. Then we calculated the DOS of the dilute Ising model to obtain a phase diagram, in good agreement with previous studies. We calculated the energy distribution, together with its first, second and fourth moments, to give the specific heat and the energy fourth order cumulant, better known as the Binder parameter, for the pure BW model. For small samples, the energy distribution displayed a doubly peaked shape, and finite size scaling analysis showed the expected reciprocal scaling of the positions of the peaks with L. The energy distribution yielded the expected BW α ≤ 2/3 critical exponent for the specific heat. The Binder parameter minimum appeared to scale with lattice size L with an exponent θB equal to the specific heat exponent. Its location (temperature) showed a large correction-to-scaling term θ1 ≤ 0.248 ± 0.025. For the dilute BW model we found a clear crossover to a single peak in the energy distribution even for small sizes and the expected α ≤ 0 was recovered.

UR - http://www.scopus.com/inward/record.url?scp=23744455988&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/38/33/004

DO - 10.1088/0305-4470/38/33/004

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AN - SCOPUS:23744455988

SN - 0305-4470

VL - 38

SP - 7253

EP - 7267

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 33

ER -