28a-WA-5 Estimation of critical exponents at the θ point in two dimensions

Miroslav Kolesik, Masuo Suzuki

V. A. Rabinovich, Yu. E. Sheludyak

Nelson A. Alves, J. R. Drugowich de Felício

In this work the two-dimensional Ising model with nearest- and next-nearest-neighbor interactions is revisited. We obtain the dynamic critical exponents z and θ from short-time Monte Carlo simulations. The dynamic critical exponent z is obtained from the time behavior of the ratio [Formula: see text], whereas the non-universal exponent θ is estimated from the time correlation of the order parameter <M(0)M(t)> ~ tθ, where M(t) is the order parameter at instant t, d is the dimension of the system and <(⋯)> is the average of the quantity (⋯) over different samples. We also obtain the static critical exponents β and ν by investigating the time behavior of the magnetization.

Daniel Harry Friedan, Zongan Qiu, Stephen H. Shenker

Roberto da Silva, Nelson A. Alves, J. R. Drugowich de Felício

The global persistence exponent theta(g) is calculated for the two-dimensional Blume-Capel model following a quench to the critical point from both disordered states and such with small initial magnetizations. Estimates are obtained for the nonequilibrium critical dynamics on the critical line and at the tricritical point. Ising-like universality is observed along the critical line and a different value theta(g)=1.080(4) is found at the tricritical point.

Th. Jolicœur, Jean-Claude Le Guillou

We show that current estimates of the critical exponents of the three-dimensional random-field Ising model are in agreement with the exponents of the pure Ising system in dimension $3\ensuremath{-}\ensuremath{\theta}$ where \ensuremath{\theta} is the exponent that governs the hyperscaling violation in the random case.