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Monte Carlo study of the Pure and Dilute Baxter-Wu model

Summary: Monte Carlo study of the Pure and Dilute
Baxter-Wu model
Nir Schreiber and Joan Adler
Physics Department, Technion, Israel Institute of Technology, Haifa, Israel, 32000
Abstract. We studied the pure and dilute Baxter-Wu (BW) models using the
Landau-Wang (LW) sampling method to calculate the Density-Of-States (DOS). We
rst 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 obtaining a phase diagram, in good
agreement with previous studies. We calculated the energy distribution, together with
its rst, second and fourth moments, to give the speci c 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. Finite size
scaling analysis, however, showed a power-law decay of the right peak with the ratio
+ = = 0:531  0:048. The energy distribution yielded the expected BW = 2=3
critical exponent for the speci c heat. The Binder parameter minimum appeared to
scale with lattice size L with an exponent  B equal to the speci c heat exponent. Its
location (temperature) showed a large correction-to-scaling term  1 = 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 = 0 was recovered.
PACS numbers: 05.10.Ln,05.50.+q,02.70.Rr


Source: Adler, Joan - Physics Department, Technion, Israel Institute of Technology


Collections: Physics