Variational renormalization method and the Potts model

M.P.M. den Nijs and H.J.F. Knops

Physica A: Statistical Mechanics and its Applications, 1978, vol. 93, issue 3, 441-456

Abstract: The variational principle is presented for a continuous renormalization transformation. It is shown that a strict application of the variational method leads to a singularity in the variational parameter which is related to that in the free energy. The equations governing the behaviour of the variational parameter can, in the continuous formulation (for a single coupling parameter), be cast in a differential form from which it can be seen that the method will predict either a very weak singularity (α < 0) or a first order transition. A numerical study of the q-state Potts model is presented which shows that as q increases to 4 the model just fails to exhibit the expected first-order transition.

Date: 1978
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:93:y:1978:i:3:p:441-456

DOI: 10.1016/0378-4371(78)90165-6

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