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Physical review. B, Condensed matter

Finite-lattice Hamiltonian results for the phase structure of the Z(q) models and the q -state Potts models

Hamzeh H. Roomany, H. W. Wyld

Published Feb 1, 1981• 45 citations
Publisher

Abstract

We use our finite-lattice approach to study the phase transitions of the Hamiltonian formulation for the (1 + 1)-dimensional $Z(q)$ models. We confirm the known result that these models possess two phases for $q<{q}_{c}$ and three phases for $q>~{q}_{c}$. Our calculation, however, gives ${q}_{c}=6$, while the perturbative calculation predicts ${q}_{c}=5$. Similar calculations for the (1 + 1)-dimensional $q$-state Potts models for $q=4, 5, \mathrm{and} 8$ failed to differentiate the second-order transition expected for $q<~4$ from the first-order transition expected for $q>~5$.

DOI
10.1103/physrevb.23.1357

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A generalization of the Niemeijer-van Leeuwen renormalization-group transformation treating disordered cells of spins as vacancies is introduced and applied to the two-dimensional qqq-state Potts model. Finite-lattice approximations yield the changeover from continuous to first-order phase transitions predicted by Baxter but not observed in previous renormalization-group calculations. Exact results are conjectured for the tricritical exponents of dilute Potts models.
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We have calculated the large-qqq expansion for the specific heat at the phase transition point in the two-dimensional q-state Potts model to the 23rd order in 1/q1/\sqrt{q}1/q​ using the finite lattice method. The series obtained allows us to give highly convergent estimates of the specific heat for q>4q>4q>4 on the first-order transition point. The result confirms the correctness of the conjecture by Bhattacharya et al. [Nucl. Phys. B 435, 526 (1995); J. Phys. I 7, 1155 (1997)] on the asymptotic behavior of the specific heat for $\stackrel{\ensuremath{\rightarrow}}{q}4.$
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