Functional RG approach to the Potts model. (11th January 2018)

• Record Type: Journal Article
• Authors: Ben Alì Zinati, Riccardo; Codello, Alessandro
• Is Part Of: Journal of statistical mechanics. (2018:Jan.)
• Publication Date: 2018-01-11
• Subjects: 16; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aa9dcc
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: The critical behavior of the ( n + 1 ) -states Potts model in d -dimensions is studied with functional renormalization group techniques. We devise a general method to derive β -functions for continuous values of d and n and we write the flow equation for the effective potential (LPA') when instead n is fixed. We calculate several critical exponents, which are found to be in good agreement with Monte Carlo simulations and ϵ-expansion results available in the literature. In particular, we focus onPercolation ( n → 0 ) andSpanning Forest ( n → − 1 ) which are the only non-trivial universality classes in d = 4, 5 and where our methods converge faster.