The McCoy-Wu Model in the Mean-field Approximation

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 $\beta \approx 3.6$ and ${\beta }_1\approx 4.1$ in the bulk and at the surface of the system, respectively. The singularity of the specific heat is characterized by an exponent $\alpha \approx -3.1$. The samples reduced critical temperature $t_c=T_c^{av}-T_c$ has a power law distribution $P(t_c)\sim t_c^{\omega }$ and we show that the difference between the values of the critical exponents in the pure and in the random system is just $\omega \approx 3.1$. Above the critical temperature the thermodynamic quantities behave analytically, thus the system does not exhibit Griffiths singularities.

LaTeX file with iop macros, 13 pages, 7 eps figures, to appear in J. Phys. A

References in corpus (1)

• Finite Temperature and Dynamical Properties of the Random Transverse-Field Ising Spin Chain

Cited by in corpus (8)

• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Strong disorder RG approach of random systems
• Smearing of the phase transition in Ising systems with planar defects
• Smeared phase transition in a three-dimensional Ising model with planar defects: Monte-Carlo simulations
• Finite temperature behavior of strongly disordered quantum magnets coupled to a dissipative bath
• Monte-Carlo study of anisotropic scaling generated by disorder
• Replica Theory of Granular Media
• Local defect in a magnet with long-range interactions