Finite-size scaling corrections in two-dimensional Ising and Potts ferromagnets

Abstract

Abstract. Finite-size corrections to scaling of critical correlation lengths and free energies of Ising and three-state Potts ferromagnets are analysed by numerical methods, on strips of width N sites of square, triangular and honeycomb lattices. Strong evidence is given that the amplitudes of the 'analytical' correction terms, N −2 , are identically zero for triangular and honeycomb Ising systems. For Potts spins, our results are broadly consistent with this lattice-dependent pattern of cancellations, though for correlation lengths non-vanishing (albeit rather small) amplitudes cannot be entirely ruled out.

Exact Universal Amplitude Ratios for Two-Dimensional Ising Models and a Quantum Spin Chain

“…The exact and numerical estimates [18] of the subdominant correction amplitudes for the sq, hc, and pt lattices are presented in Table I, which shows that the numerical values obtained by de Queiroz [18] are very close to our exact results. On the basis of conformal invariance, the asymptotic finite-size scaling behavior of the critical free energy and the inverse correlation length is found to be [19] …”

High-precision estimate ofg4in the 2D Ising model

“…Note that this is expected to be true only in the thermodynamic limit. In the finite-size scaling limit corrections that vanish like L −2 1 are indeed observed [11]. It is also not true for other observables, for instance, for the correlation length ξ.…”

Finite-size scaling and corrections in the Ising model with Brascamp-Kunz boundary conditions

“…Typically, numerically based or experimental studies involve systems of limited size where these corrections to leading FSS behaviour cannot be dismissed. A better knowledge of universal sub-dominant behaviour would therefore be of great benefit in FSS extrapolation procedures [13,14,15,16,17,18,19,20,21,22]. …”