The quenched site-diluted Ising ferromagnet, with a probability p for site occupation, is studied on a square lattice. A method, based on self-organized criticality, drives the system spontaneously to the critical point, providing an efficient way to estimate critical properties for different...

A special quantum-group oscillator presents an upper bound in its energy spectrum, which is preceded by an accumulation of infinite levels. The standard Boltzmann–Gibbs (BG) statistical-mechanics formalism is inadequate for dealing with such systems, since the partition function diverges for...

We use the replica method to investigate the behavior of an infinite-range mixed-spin (spin-12 and spin-1) Ising glass in the presence of a crystal field. The properties of the model are described in terms of two sets of order parameters. We obtain the replica-symmetric spin-glass solutions and...

A p-spin interaction Ashkin–Teller spin glass, with three independent Gaussian probability distributions for the exchange interactions, is studied by means of the replica method. A simple phase diagram is obtained within the replica-symmetric approximation, presenting an instability of the...

Microscopic models, which resemble random magnetic systems, have been used recently in the literature for the description of financial markets. In the present work, a model with many interacting agents, similar to an Ising random magnet with infinite-range interactions, is investigated. The...

The critical properties of short-range Ising spin-glass models, defined on diamond hierarchical lattices of graph fractal dimensions df=2.58,3, and 4, and scaling factor 2, are studied via a method based on the Migdal–Kadanoff renormalization-group scheme. The order-parameter critical exponent...

By considering a simple thermodynamic system, in thermal equilibrium at a temperature T and in the presence of an external parameter A, we focus our attention on the particular thermodynamic (macroscopic) relation dU=TdS+δW. Using standard axioms from information theory and the fact that the...

A method for obtaining critical properties is presented. Based on self-organized criticality, it drives the system spontaneously to the critical point, providing an efficient way to estimate critical properties. The method is illustrated for Ising spin systems, and despite the small lattice...

We consider a mixed spin-glass model defined in terms of two groups of spins, XY and p-state clock variables, respectively; the interactions are infinite-range-like and between distinct groups only. An anisotropy parameter Dp, which favours p directions in the plane, is introduced for the XY...