Exact Finite Method of Lattice Statistics. V. The Thermodynamic Phases of a Triangular Lattice Gas

Runnels, L. K.; Craig, J. R.; Streiffer, H. R.

doi:10.1063/1.1675131

Cited by 23 publications

(3 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Next, we study the triangular lattice N2 model (exclusion up to the next-nearest-neighbor). This model was long ago investigated, and early studies suggested that the phase transition is first order [25,26,27]. However, later transfer matrix analysis [28], and recent exhaustive MC results [29] concluded that the model undergoes a second order phase transition at µ c = 1.75682(2) and critical density ρ c = 0.180(4), and is believed to be part of the q = 4 Potts universality class, with σ ′ = 1/3.…”

Section: B Triangular Lattice N2 Modelmentioning

confidence: 99%

Critical exponents from cluster coefficients

Rotman

Eisenberg

2009

Phys. Rev. E

View full text Add to dashboard Cite

For a large class of repulsive interaction models, the Mayer cluster integrals can be transformed into a tridiagonal real symmetric matrix R_{mn} , whose elements converge to two constants. This allows for an effective extrapolation of the equation of state for these models. Due to a nearby (nonphysical) singularity on the negative real z axis, standard methods (e.g., Padé approximants based on the cluster integrals expansion) fail to capture the behavior of these models near the ordering transition, and, in particular, do not detect the critical point. A recent work [E. Eisenberg and A. Baram, Proc. Natl. Acad. Sci. U.S.A. 104, 5755 (2007)] has shown that the critical exponents sigma and sigma;{'} , characterizing the singularity of the density as a function of the activity, can be exactly calculated if the decay of the R matrix elements to their asymptotic constant follows a 1/n;{2} law. Here we employ renormalization group (RG) arguments to extend this result and analyze cases for which the asymptotic approach of the R matrix elements toward their limiting value is of a more general form. The relevant asymptotic correction terms (in RG sense) are identified, and we then present a corrected exact formula for the critical exponents. We identify the limits of usage of the formula and demonstrate one physical model, which is beyond its range of validity. The formula is validated numerically and then applied to analyze a number of concrete physical models.

show abstract

Section: B Triangular Lattice N2 Modelmentioning

confidence: 99%

Critical exponents from cluster coefficients

Rotman

Eisenberg

2009

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…The LG34 model resembles the phase behavior of the purely repulsive lattice-gas model studied in [16], hereby called LG3, where particles exclude first-and second-neighbor sites on a triangular lattice while softly repelling each other at third-neighbor distance. Both models share the same phases, although LG34 is more effective in promoting the stability of the solids at the expense of the fluid.…”

Section: A Lg34 Modelmentioning

confidence: 99%

Inverse melting in lattice-gas models

Prestipino

2007

Phys. Rev. E

View full text Add to dashboard Cite

Inverse melting is the phenomenon, observed in both helium isotopes, by which a crystal melts when cooled at constant pressure. I investigate discrete-space analogs of inverse melting by means of two instances of a triangular-lattice-gas system endowed with a soft-core repulsion and a short-ranged attraction. To reconstruct the phase diagram, I use both transfer-matrix and Monte Carlo methods, as well as low-temperature series expansions. In one case, a phase behavior reminiscent of helium emerges, with a loose-packed phase (which is solidlike for low temperatures and liquidlike for high temperatures) extending down to zero temperature for low pressures and the possibility of melting the close-packed solid by isobaric cooling. At variance with previous model studies of inverse melting, the driving mechanism of the present phenomenon is mainly geometrical, related to the larger free-energy cost of a "vacancy" in the loose-packed solid than in the close-packed one.

show abstract

“…Thus, one would expect that, if it is second order, the melting of ordered phase should be in the 4-state Potts universality class. However, several studies at the end of 60s last century suggested that the phase transition is first order [8,9]. Later, Bartelt and Einstein [10] reexamined this model by a phenomenological renormalization-transfer-matrix scaling.…”

Section: Introductionmentioning

confidence: 99%

A Monte Carlo study of the triangular lattice gas with the first- and the second-neighbor exclusions

Zhang,

Deng

2008

Preprint

View full text Add to dashboard Cite

We formulate a Swendsen-Wang-like version of the geometric cluster algorithm. As an application, we study the hard-core lattice gas on the triangular lattice with the first-and the second-neighbor exclusions. The data are analyzed by finite-size scaling, but the possible existence of logarithmic corrections is not considered due to the limited data. We determine the critical chemical potential as µ c = 1.75682(2) and the critical particle density as ρ c = 0.180(4). The thermal and magnetic exponents y t = 1.51(1) ≈ 3/2 and y h = 1.8748(8) ≈ 15/8, estimated from Binder ratio Q and susceptibility χ, strongly support the general belief that the model is in the 4-state Potts universality class. On the other hand, the analyses of energy-like quantities yield the thermal exponent y t ranging from 1.440(5) to 1.470(5). These values differ significantly from the expected value 3/2, and thus imply the existence of logarithmic corrections.

show abstract

Exact Finite Method of Lattice Statistics. V. The Thermodynamic Phases of a Triangular Lattice Gas

Cited by 23 publications

References 14 publications

Critical exponents from cluster coefficients

Critical exponents from cluster coefficients

Inverse melting in lattice-gas models

A Monte Carlo study of the triangular lattice gas with the first- and the second-neighbor exclusions

Contact Info

Product

Resources

About