The McCoy-Wu model in the mean-field approximation

Abstract

Abstract. We consider a system with randomly layered ferromagnetic bonds (McCoy-Wu model) and study its critical properties in the frame of mean-field theory. In the low-temperature phase there is an average spontaneous magnetization in the system, which vanishes as a power law at the critical point with the critical exponents β ≈ 3.6 and β1 ≈ 4.1 in the bulk and at the surface of the system, respectively. The singularity of the specific heat is characterized by an exponent α ≈ −3.1. The samples reduced critical temperature tc = T av c − Tc has a power law distribution P(tc) ∼ t ω c and we show that the difference between the values of the critical exponents in the pure and in the random system is just ω ≈ 3.1. Above the critical temperature the thermodynamic quantities behave analytically, thus the system does not exhibit Griffiths singularities.