High-precision estimate ofg4in the 2D Ising model

High-precision estimate of g4 in the 2D Ising model

We compute the renormalized four-point coupling in the 2d Ising model using transfer-matrix techniques. We greatly reduce the systematic uncertainties which usually affect this type of calculations by using the exact knowledge of several terms in the scaling function of the free energy. Our final result is g4 = 14.69735(3).

The solution of the 2D Ising model

The Surface Tension near Criticality of the 2d-ising Model

For the two dimensional Ising model, we construct the adequate surface tension near criticality. The latter quantity has been shown [9] to play a central role in the study of phase coexistence in a joint limit where the temperature approaches the critical point from below and simultaneously the size of the system increases fast enough.

The critical equation of state of the 2D Ising model

We compute the 2n-point coupling constants in the high-temperature phase of the 2d Ising model by using transfer-matrix techniques. This provides the first few terms of the expansion of the effective potential (Helmholtz free energy) and of the equation of state in terms of the renormalized magnetization. By means of a suitable parametric representation, we determine an analytic extension of th...

Duality of the 2D Nonhomogeneous Ising Model on the Torus

Duality relations for the 2D nonhomogeneous Ising model on the finite square lattice wrapped on the torus are obtained. The partition function of the model on the dual lattice with arbitrary combinations of the periodical and antiperiodical boundary conditions along the cycles of the torus is expressed through some specific combination of the partition functions of the model on the original lat...