Finite size and boundary effects in critical two-dimensional free-fermion models

  title={Finite size and boundary effects in critical two-dimensional free-fermion models},
  author={Nikolay Sh. Izmailian},
  journal={The European Physical Journal B},
  • N. Izmailian
  • Published 28 August 2017
  • Physics
  • The European Physical Journal B
Abstract Here we will consider the finite-size scaling, finite-size corrections and boundary effects for the critical two-dimensional free-fermion models. A short review of significant achievements and possibilities is given. However, this review is still far from completeness. We derive the exact finite-size corrections for the set of free models of statistical mechanics, including Ising model, dimer model, resistor network and spanning tree model under different boundary conditions. We have… 
3 Citations
Finite-size correction to the scaling of free energy in the dimer model on a hexagonal domain
We consider dimer model on a hexagonal lattice. This model can be seen as a "pile of cubes in the box". The energy of configuration is given by the volume of the pile and the partition function is
Investigation of Finite-Size 2D Ising Model with a Noisy Matrix of Spin-Spin Interactions
Analysis of changes in the thermodynamic properties of a spin system when it passes from the classical two-dimensional Ising model to the spin glass model, where spin-spin interactions are random in their values and signs shows that when the variance of the noise reaches one, there is a jump of the ground state from the fully correlated state to an uncorrelated state.
Specific heat and partition function zeros for the dimer model on the checkerboard B lattice: Finite-size effects.
The partition function of the dimer model on a 2M×2N checkerboard B lattice wrapped on a torus is analyzed and very unusual behavior of the partition function zeros and the specific heat of the Dimer model is found.


Exact finite-size-scaling corrections to the critical two-dimensional Ising model on a torus: II. Triangular and hexagonal lattices
We compute the finite-size corrections to the free energy, internal energy and specific heat of the critical two-dimensional spin-1/2 Ising model on triangular and hexagonal lattices wrapped on a
Finite-size scaling for the ising model on the Möbius strip and the klein bottle.
The relation to the finite-size correction calculations for the dimer statistics is discussed and interesting aspect-ratio dependence of the value of the Binder parameter at T = T(c) for various boundary conditions is found.
Finite-size scaling and corrections in the Ising model with Brascamp-Kunz boundary conditions
The Ising model in two dimensions with the special boundary conditions of Brascamp and Kunz is analyzed. Leading and subdominant scaling behavior of the Fisher zeros are determined exactly. The exact
Exact finite-size corrections for the spanning-tree model under different boundary conditions.
  • N. Izmailian, R. Kenna
  • Mathematics, Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2015
The exact asymptotic expansions of the logarithm of the partition function for each case of the spanning tree under free-boundary conditions are derived.
Conformal invariance, the central charge, and universal finite-size amplitudes at criticality.
We show that for conformally invariant two-dimensional systems, the amplitude of the finite-size corrections to the free energy of an infinitely long strip of width L at criticality is linearly
Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional 4-State Potts Model
We analyze the scaling and finite-size-scaling behavior of the two-dimensional 4-state Potts model. We find new multiplicative logarithmic corrections for the susceptibility, in addition to the
Exact finite-size corrections for the square-lattice Ising model with Brascamp-Kunz boundary conditions.
Finite-size scaling, finite-size corrections, and boundary effects for critical systems have attracted much attention in recent years. Here we derive exact finite-size corrections for the free energy