Published in

IOP Publishing, Journal of Physics A: Mathematical and Theoretical, 40(41), p. 405004

DOI: 10.1088/1751-8113/41/40/405004

Links

Tools

Export citation

Search in Google Scholar

Alternative description of the 2D Blume-Capel model using Grassmann algebra

Journal article published in 2008 by Maxime Clusel, Jean-Yves Fortin ORCID, Vladimir N. Plechko
This paper is available in a repository.
This paper is available in a repository.

Full text: Download

Green circle
Preprint: archiving allowed
Upload
Orange circle
Postprint: archiving restricted
Upload
Red circle
Published version: archiving forbidden
Policy details
Data provided by SHERPA/RoMEO

Abstract

We use Grassmann algebra to study the phase transition in the two-dimensional ferromagnetic Blume-Capel model from a fermionic point of view. This model presents a phase diagram with a second order critical line which becomes first order through a tricritical point, and was used to model the phase transition in specific magnetic materials and liquid mixtures of He$^3$-He$^4$. In particular, we are able to map the spin-1 system of the BC model onto an effective fermionic action from which we obtain the exact mass of the theory, the condition of vanishing mass defines the critical line. This effective action is actually an extension of the free fermion Ising action with an additional quartic interaction term. The effect of this term is merely to render the excitation spectrum of the fermions unstable at the tricritical point. The results are compared with recent numerical Monte-Carlo simulations. Comment: 32 pages, 2 figures;