6533b7dbfe1ef96bd1270008
RESEARCH PRODUCT
The McCoy-Wu model in the mean-field approximation
Pierre Emmanuel BerchePierre Emmanuel BercheFerenc IglóiGábor PalágyiBertrand Berchesubject
PhysicsStatistical Mechanics (cond-mat.stat-mech)FOS: Physical sciencesGeneral Physics and AstronomyStatistical and Nonlinear PhysicsDisordered Systems and Neural Networks (cond-mat.dis-nn)Condensed Matter - Disordered Systems and Neural NetworksPower lawOmegaSingularityMean field theoryCritical point (thermodynamics)ExponentSpontaneous magnetizationCritical exponentCondensed Matter - Statistical MechanicsMathematical PhysicsMathematical physicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1998-06-12 | Journal of Physics A: Mathematical and General |