Eur. Phys. J. B (2012) 85: 258
https://doi.org/10.1140/epjb/e2012-30051-1

Regular Article

Dynamical and stationary critical behavior of the Ising ferromagnet in a thermal gradient

¹ Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), CCT La Plata, CONICET, UNLP, Calle 59 No. 789, 1900 La Plata, Argentina
² Departamento de Física, Facultad de Ciencias Exactas, UNLP, 1900 La Plata, Argentina

^a e-mail: ezequielalb@yahoo.com.ar

Received: 19 January 2012
Received in final form: 22 May 2012
Published online: 30 July 2012

Abstract

In this paper we present and discuss results of Monte Carlo numerical simulations of the two-dimensional Ising ferromagnet in contact with a heat bath that intrinsically has a thermal gradient. The extremes of the magnet are at temperatures T₁ < T_c < T₂, where T_c is the Onsager critical temperature. In this way one can observe a phase transition between an ordered phase (T < T_c) and a disordered one (T > T_c) by means of a single simulation. By starting the simulations with fully disordered initial configurations with magnetization m ≡ 0 corresponding to T = ∞, which are then suddenly annealed to a preset thermal gradient, we study the short-time critical dynamic behavior of the system. Also, by setting a small initial magnetization m = m₀, we study the critical initial increase of the order parameter. Furthermore, by starting the simulations from fully ordered configurations, which correspond to the ground state at T = 0 and are subsequently quenched to a preset gradient, we study the critical relaxation dynamics of the system. Additionally, we perform stationary measurements (t → ∞) that are discussed in terms of the standard finite-size scaling theory. We conclude that our numerical simulation results of the Ising magnet in a thermal gradient, which are rationalized in terms of both dynamic and standard scaling arguments, are fully consistent with well established results obtained under equilibrium conditions.