arXiv subjects

A. Pelizzola

Publications and source records attributed to A. Pelizzola.

22 records · Page 2Linked to original sources

arXiv1994

Cluster Variation Method, Pade` Approximants and Critical Behaviour

In the present paper we show how non--classical, quite accurate, critical exponents can be extracted in a very simple way from the Padé analysis of the results obtained by mean field like approximation schemes, and in particular by the cluster variation method. We study the critical behavior of the Ising model on several lattices (quadratic, triangular, simple cubic and face centered cubic) and two problems of surface critical behaviour. Both unbiased and biased approximants are used, and results are in very good agreement with the exact or numerical ones.

cond-mat↗

arXiv1993

Mean Field Renormalization Group for the Boundary Magnetization of Strip Clusters

We analyze in some detail a recently proposed transfer matrix mean field approximation which yields the exact critical point for several two dimensional nearest neighbor Ising models. For the square lattice model we show explicitly that this approximation yields not only the exact critical point, but also the exact boundary magnetization of a semi--infinite Ising model, independent of the size of the strips used. Then we develop a new mean field renormalization group strategy based on this approximation and make connections with finite size scaling. Applying our strategy to the quadratic Ising and three--state Potts models we obtain results for the critical exponents which are in excellent agreement with the exact ones. In this way we also clarify some advantages and limitations of the mean field renormalization group approach.

cond-mat↗

arXiv1993

Low-Temperature Expansion for a First Order Surface Transition

The question concerning the possibility of a first order surface transition in a semi--infinite Blume--Capel model is addressed by means of low temperature expansions. It is found that such a transition can exist, according to mean field and cluster variation approximations, and contrarily to renormalization group results.

cond-mat↗

arXiv1993

Cluster Variation Approach to the Random-Anisotropy Blume-Emery-Griffiths Model

The random--anisotropy Blume--Emery--Griffiths model, which has been proposed to describe the critical behavior of $^3$He--$^4$He mixtures in a porous medium, is studied in the pair approximation of the cluster variation method extended to disordered systems. Several new features, with respect to mean field theory, are found, including a rich ground state, a nonzero percolation threshold, a reentrant coexistence curve and a miscibility gap on the high $^3$He concentration side down to zero temperature. Furthermore, nearest neighbor correlations are introduced in the random distribution of the anisotropy, which are shown to be responsible for the raising of the critical temperature with respect to the pure and uncorrelated random cases and contribute to the detachment of the coexistence curve from the $λ$ line.

cond-mat↗