M.Sc Student | Schreiber Nir |
---|---|

Subject | Monte-Carlo Study of the Baxter-Wu Model |

Department | Department of Physics |

Supervisor | Dr. Joan Adler |

We studied the pure and dilute Baxter-Wu models
using the Landau-Wang (LW) sampling method to calculate the Density-Of-States. For
the pure case, the energy distribution together with its second and fourth
moments were calculated to give the specific heat and the reduced energy fourth
order cumulant, *B*, better known as the Binder parameter. The energy
distribution displayed a doubly peaked shape. Finite size scaling analysis,
however, showed a power low decay of the distance between these peaks to
eventually vanish for _{}. It also yielded the expected
Baxter-Wu _{} critical
exponent. The Binder parameter minimum appeared to scale with lattice size *L*
, with an exponent _{} identical with the specific heat
exponent and the position (temperature) of the Binder parameter minimum
appeared to show a large correction-to-scaling term _{}. We then introduced
impurities to the Baxter-Wu model and calculated the phase diagram in
concentration-temperature plane. Our results, obtained by locating the specific
heat maxima, were reliable for low impurities concentrations only, because of
small energy fluctuations, characteristic to systems with high amount of
disorder, which caused to broader and wider peaks of the specific heat. For
the dilute Baxter-Wu model we found a clear crossover to a single peak in the
energy distribution even for small lattice sizes and the expected _{} was
recovered. The Density-Of-States of the two-dimensional Ising model were also
calculated and were compared to the exact result. The phase diagram of the
dilute two-dimensional Ising model was also calculated and showed good
agreement with previous results.