Irrelevant interactions without composite operators: a remark on the universality of second-order phase transitions.

DOI10.1088/0305-4470/34/13/302zbMATH Open1063.82519arXivcond-mat/0007476OpenAlexW3099019017MaRDI QIDQ2716567

Christoph Kopper, W. Pedra

Publication date: 2001

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Abstract: We study the critical behaviour of symmetric $ph{i}_4^4$ theory including irrelevant terms of the form $ph{i}^{4+2n}/Lambd{a}_0^{2n}$ in the bare action, where $Lambd{a}_0$ is the UV cutoff (corresponding e.g. to the inverse lattice spacing for a spin system). The main technical tool is renormalization theory based on the flow equations of the renormalization group which permits to establish the required convergence statements in generality and rigour. As a consequence the effect of irrelevant terms on the critical behaviour may be studied to any order without using renormalization theory for composite operators. This is a technical simplification and seems preferable from the physical point of view. In this short note we restrict for simplicity to the symmetry class of the Ising model, i.e. one component $ph{i}_4^4$ theory. The method is general, however.

Full work available at URL: https://arxiv.org/abs/cond-mat/0007476

Mathematics Subject Classification ID

Phase transitions (general) in equilibrium statistical mechanics (82B26) Renormalization group methods in equilibrium statistical mechanics (82B28) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

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