Fermionic Structure of Two-Dimensional Ising Model with Quenched Site Dilution

Abstract

We apply a new anticommuting path integral technique to clarify the fermionic structure of the 2D Ising model with quenched site dilution. In the $N$-replica scheme, the model is explicitly reformulated as a theory of interacting fermions on a lattice. An unusual feature is that the leading term of interaction in the exact lattice theory is of order $2N$ in fermions, where $N$ is the number of replicas. The continuum-limit approximation near $T_c$ for weak dilution produces, however, an effective four-fermion interaction. In particular, this implies the doubled-logarithmic singularity in the specific heat near $T_c$ for weak site dilution. The exact value of the initial slope is also obtained. Keywords: Ising model, site disorder, anticommuting Grassmann variables

LaTeX, 1 + 14 pages, no figures

Cited by in corpus (12)

• Scaling Relations for Logarithmic Corrections
• Self-Consistent Scaling Theory for Logarithmic Correction Exponents
• Critical behaviour of the 2d spin diluted Ising model via the equilibrium ensemble approach
• Specific heat of two-dimensional diluted magnets
• Universality and multifractal behaviour of spin-spin correlation functions in disordered Potts models
• Scaling Analysis of the Site-Diluted Ising Model in Two Dimensions
• The critical amplitude ratio of the susceptibility in the random-site two-dimensional Ising model
• Scaling and finte-size-scaling in the two dimensional random-coupling Ising ferromagnet
• Alternative description of the 2D Blume-Capel model using Grassmann algebra
• Logarithmic corrections in the two-dimensional Ising model in a random surface field
• Fermions and Disorder in Ising and Related Models in Two Dimensions
• Itinerant electrons on dilute frustrated Ising lattices