Journal of Physics A Mathematical and General

Latent heats from finite-size scaling

Chris J. Hamer

Published Sep 11, 1983• 18 citations

Abstract

A method of obtaining the latent heat at a first-order transition from finite-lattice matrix elements is discussed, and demonstrated for the case of the (1+1)D Potts model. The method is shown to provide smoothly convergent finite-lattice sequences. The structure of the finite-lattice Hamiltonian eigenvalues is exhibited, and a characteristic signal of the first-order transition is proposed. The finite-size scaling behaviour at the transition is also discussed.

DOI: 10.1088/0305-4470/16/13/033

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Journal of Physics A Mathematical and General

Latent heats from finite-size scaling

Chris J. Hamer

Published Sep 11, 1983• 18 citations

Publisher

Abstract

DOI: 10.1088/0305-4470/16/13/033

Related papers

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Chris J. Hamer, J. Oitmaa, Z Weihong

Journal of Physics A Mathematical and GeneralApr 7, 199211 citations

{\mathit{T}}_{0}

(V) have recently been proposed which involve only exponential corrections with respect to

{\mathit{T}}_{0}

\ensuremath{\equiv}

{\mathit{T}}_{0}

(\ensuremath{\infty}). One of these approaches suggests also a different and efficient way to compute the latent heat. These propositions are tested for the temperature-driven first-order phase transitions in the two-dimensional q-state Potts model for q=5, 8, and 10 by means of Monte Carlo simulations, using the single-cluster update algorithm and histogram reweighting techniques.

{\mathit{L}}^{3}

block lattices (L up to size 36) and obtain high-precision estimates for the leading partition-function zeros. The finite-size-scaling analysis of the first zero exhibits the expected convergence of the critical exponent \ensuremath{\nu} toward 1/D for large L; in particular, we find \ensuremath{\nu}=2.955(26) from our two largest lattices. Analysis of our specific-heat

{\mathit{C}}_{\mathit{v}}

data yields l=0.080 31(26) for the latent heat. Along another line of approach, we calculate the mass gap m=1/\ensuremath{\xi} (\ensuremath{\xi} is the correlation length) for cylindrical

{\mathit{L}}^{2}

{\mathit{L}}_{\mathit{z}}

lattices (L up to 24 and

{\mathit{L}}_{\mathit{z}}

=256). The finite size-scaling analysis of these results is also consistent with the convergence of \ensuremath{\nu} toward 1/D, but that the limiting value is 1/D is not yet conclusively established. Some theoretical arguments favor \ensuremath{\nu}\ensuremath{\rightarrow}0 in case of a first-order transition in a cylindrical ${\mathit{L}}^{\mathit{D}\mathrm{\ensuremath{-}}1}$\ensuremath{\infty} geometry. Therefore, we also applied our approach to the 2D ten-state Potts model, which is known to have a strong first-order transition. In this case we find unambiguous evidence in favor of 1/D as the limiting value.