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Weak universality, bicritical points and reentrant transitions in the critical behaviour of a mixed spin‐1/2 and spin‐3/2 Ising model on the Union Jack (centered square) lattice
Author(s) -
Strečka Jozef
Publication year - 2006
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200541318
Subject(s) - ising model , square lattice , physics , condensed matter physics , renormalization group , universality (dynamical systems) , critical exponent , bounded function , critical line , vertex (graph theory) , mathematics , spin model , mathematical physics , combinatorics , phase transition , mathematical analysis , graph
The mixed spin‐1/2 and spin‐3/2 Ising model on the Union Jack lattice is solved by establishing a mapping correspondence with the eight‐vertex model. It is shown that the model under investigation becomes exactly soluble as a free‐fermion eight‐vertex model when the parameter of uniaxial single‐ion anisotropy tends to infinity. Under this restriction, the critical points are characterized by critical exponents from the standard Ising universality class. In a certain subspace of interaction parameters, which corresponds to a coexistence surface between two ordered phases, the model becomes exactly soluble as a symmetric zero‐field eight‐vertex model. This surface is bounded by a line of bicritical points having interaction‐dependent critical exponents that satisfy a weak universality hypothesis. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)