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03-08E

03-08E


By icmp_admin - Posted on 08 February 2012

UDC: 
530.145
PACS: 
05.50.+q, 64.60.Cn, 75.10.Hk

Mathematical theory of the Ising model and its generalizations: an introduction

Yu. Kozitsky

An introduction into the rigorous theory of equilibrium states of a number of lattice models of classical and quantum statistical physics is given. Generalized Ising models with discrete, continuous, bounded and unbounded spins, translation invariant and with a hierarchical structure; quantum spin models, models of interacting quantum anharmonic oscillators are considered. For the classical models, certain properties of local Gibbs states, such as the Lee-Yang theorem, correlation inequalities, phase transitions, self-similarity, are discussed. For the quantum models, an approach based on functional integration is presented on an introductory level.

Year: 
2003
Pages: 
67
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