Stability of critical behaviour, critical-exponent renormalization and first-order transitions

H.W. Capel, L.W.J. Den Ouden and J.H.H. Perk

Physica A: Statistical Mechanics and its Applications, 1979, vol. 95, issue 3, 371-416

Abstract: The critical behaviour of systems with short-range interactions in which the free energy has divergent second derivatives is shown to be unstable under small perturbations. The perturbations can arise from additional terms in the hamiltonian with a long-range nature, but also from hidden variables, subjected to constraints. In general there will be either critical-exponent renormalization or first-order transitions; in special cases one can also have more complicated multicritical behaviour. In the analysis use is made of Legendre transformations and homogeneity properties of the short-range system. The results are rather general and independent of specific properties of operators in the hamiltonian, or the nature and number of hidden variables.

Date: 1979
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:95:y:1979:i:3:p:371-416

DOI: 10.1016/0378-4371(79)90024-4

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