Critical fluctuations for quantum mean-field models

N Angelescu, M. Bundaru

The spin probability distribution at equilibrium in a multicomponent mean-field model of a ferromagnetic slab made of N rows is considered. Everywhere, but at the critical point, the spin fluctuations converge, as the number of spins pet row tends to infinity , to Gaussians with covariance equal to the thermodynamic susceptibility matrix. At criticality, abnormal coherent fluctuations along the positive eigenvector of the interaction matrix are found, whose limit distribution is an exp(-x 4 ) law.

A.K. Callebaut, M. Fannes

Igor Rodnianski, Benjamin Schlein

Terufumi Yokota

Fluctuations can break down mean-field critical behaviour. For the random-field Ising model, fluctuations caused by the randomness are important. The Ginzburg criteria based on two kinds of mean-field theory are discussed. One is the mean-field theory using the replica method and the other is the site-dependent mean-field theory. An argument that justifies the use of the site-dependent mean-field theory to obtain critical properties for the random-field Ising model is given.

Hangmo Yi

We study the effect of quantum fluctuations on the critical behavior of the Ising ferromagnetic phase transitions that do not belong to the mean-field universality class. A model system is considered, in which Ising spins are placed on the nodes of a scale-free network. Our Monte Carlo analysis shows that the critical exponents differ from those of mean-field phase transitions when degree exponent gamma is in the range 3<gamma<5 . This confirms earlier analytic calculations based on ansatzes and approximation methods. As we apply quantum fluctuations by means of a magnetic field perpendicular to the Ising spin direction, the transition temperature T(c) decreases with increasing magnetic field strength. We find, however, that the quantum fluctuations do not alter the critical exponents and the universality class remains unchanged.

Dimo I. Uzunov, E. R. Kokutcheva, YONKO T. MILLEV