2008/03/31 by Maxime Clusel, Jean-Yves Fortin, V. N. Plechko +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Action (physics) #Algebra over a field #Complex Systems and Time Series Analysis #Condensed matter physics #Critical line #Critical phenomena #Exterior algebra #Fermion #Ising model #Mathematical physics #Mathematics #Phase (matter) #Phase diagram #Phase transition #Physics #Pure mathematics #Quantum many-body systems #Quantum mechanics #Quartic function #Statistical physics #Theoretical and Computational Physics #Tricritical point #cond-mat.other #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8113/41/40/405004
published as Journal of Physics A: Mathematical and Theoretical, vol 41, p 405004 (2008); · 32 pages, 2 figures;
openalex publication_date 2008/09/11 · arxiv created 2008/10/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract. We use Grassmann algebra to study the phase transition of the 2D Blume-Capel 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 liquid mixtures of He3-He4. In particular, we are able to map the spin-1 system onto an effective fermionic action from which we obtain the exact mass of the theory. 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 to render the excitation spectrum of the fermions unstable at the tricritical point.