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Physical review. B, Condensed matter

Floating phase in the chiral Potts model. A Monte Carlo renormalization-group analysis

J. M. Houlrik, Svend J. Knak Jensen, Per Bak

Published Sep 1, 1983• 14 citations
Publisher

Abstract

Layers of atoms or molecules adsorbed on surfaces may exhibit floating critical phases. To investigate this phenomenon we have developed a Monte Carlo renormalization-group scheme and performed calculations on the three-state chiral Potts model. The results indicate a continuous transition from a floating phase to a liquid phase at a temperature much higher than that found by series-expansion methods.

DOI
10.1103/physrevb.28.2883

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Layers of atoms or molecules adsorbed on surfaces may exhibit floating critical phases. To investigate this phenomenon we have developed a Monte Carlo renormalization-group scheme and performed calculations on the three-state chiral Potts model. The results indicate a continuous transition from a floating phase to a liquid phase at a temperature much higher than that found by series-expansion methods.
A Monte Carlo renormalization-group scheme based on a ``floating sublattice'' blocking rule is constructed for the two-dimensional three-state chiral clock model. The presence of a critical phase is established by matching certain wave-vector-dependent correlation functions derived from lattices differing in linear size by a factor of 2. The wave vector, which in a function of temperature and the asymmetry parameter \ensuremath{\Delta}, is determined from the simulations. For \ensuremath{\Delta}=0.45, a critical phase is established in a temperature range. For \ensuremath{\Delta}=0.35, no critical phase is observed, suggesting that the phase diagram has a Lifschitz point in the interval 0.35<\ensuremath{\Delta}<0.45. Alternatively, the wave vector and the width of the critical phase at \ensuremath{\Delta}=0.35 are much smaller than for \ensuremath{\Delta}=0.45..AE
Many condensed matter systems, ranging from adsorbed surfaces to bulk magnets, are microscopically modelled by interacting q-state Potts spins, arrayed in d dimensions. A changeover from second-order phase transitions at q≤qc(d) to first-order transitions at q≳qc can be understood as a condensation of effect vacancies, which are patches of local disorder favored by entropy. Accordingly, the renormalization-group treatment of Potts models is within context of Potts-lattice-gas models, where critical and tricritical fixed points occur at low q, but merge and annihilate at qc. This picture has led to exact tricritical exponents in two dimensions. It is also consistent with recent experimental results on intercalated systems in three dimensions. Effective vacancies in pure Potts models have also been studied by Monte Carlo simulation. Their effective chemical potential can be controlled by a four-point interaction, which proved useful in Monte Carlo renormalization-group studies.
The critical behavior of the three-state Potts model in two dimensions is investigated with the use of the Monte Carlo renormalization group (MCRG), and the results are compared with conjectured values as well as with other methods. Recent advances in the MCRG enable greatly improved convergence, as well as greater insight into the structure of the renormalization transformation. The introduction of a four-point interaction is used to control the chemical potential of effective vacancies in a purely Potts Hamiltonian.