Universality Away from Critical Points in Two-Dimensional Phase Transitions

Lapilli, Cintia; Pfeifer, Peter; Wexler, Carlos

doi:10.1103/physrevlett.96.140603

Cited by 83 publications

(102 citation statements)

References 24 publications

(49 reference statements)

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“…The intermediate planar phase was found in a similar triangular AFM BC model 36 and the planar rotator (p-state clock) model 47,51 at not very large values of p. Our analysis of the BL model demonstrates that the high temperature peak of C v represents the second order phase transition in the three-state Potts universality class and the low-temperature peak is due to Schottky anomaly.…”

Section: Discussionmentioning

confidence: 79%

“…The six-state model can exhibit either a first-order transition, two BKT-type transitions, or successive Ising, three-state Potts, or Ashkin-Teller-type transitions 50 . The competition of the NN AFM interactions and NNN FM interactions in the TAFI model leads to a two-peaked temperature dependence of a specific heat 43 framing the planar phase in a similar manner as for the q-state clock models 51 .…”

Section: Introductionmentioning

confidence: 99%

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Phase transition properties of the Bell-Lavis model

2014

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Using Monte Carlo calculations we analyze the order and the universality class of phase transitions into a low density (honeycomb) phase of a triangular antiferromagnetic three-state Bell-Lavis model. The results are obtained in a whole interval of chemical potential µ corresponding to the honeycomb phase. Our results demonstrate that the phase transitions might be attributed to the three-state Potts universality class for all µ values except for the edges of the honeycomb phase existence. At the honeycomb phase and the low density gas phase boundary the transitions become of the first order. At another, honeycomb-to-frustrated phase boundary, we observe the approach to the crossover from the three-state Potts to the Ising model universality class. We also obtain the Schottky anomaly in the specific heat close to this edge. We show that the intermediate planar phase, found in a very similar antiferromagnetic triangular Blume-Capel model, does not occur in the Bell-Lavis model.

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Section: Discussionmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Phase transition properties of the Bell-Lavis model

2014

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“…The Ising model with competing short-range and long-range interactions and the planar (XY , KosterlitzThouless) model with p-fold symmetry breaking orientational field [19,20] are rather similar. For the planar model very different predictions for the cases p = 4 (square lattice) and p = 6 (hexagonal lattice) are drawn.…”

Section: Introductionmentioning

confidence: 99%

“…For the planar model very different predictions for the cases p = 4 (square lattice) and p = 6 (hexagonal lattice) are drawn. In the latter case the phase transition sequence disordered → isotropic quasiliquid → ordered phase is anticipated with decrease of temperature [19,20]. In the case of a square lattice the intermediate phase is expected to have a vanishingly small stability region.…”

Section: Introductionmentioning

confidence: 99%

Modelling of thermodynamical and dynamical properties of magnetic stripes on 2D hexagonal lattice

Joknys¹

2007

Lithuanian J. Phys.

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The model with competing exchange J and dipole-dipole D interactions on 2D hexagonal lattice is studied using Monte Carlo method. We calculate the energy, specific heat, order parameter, and susceptibility of the system close to the phase transition point Tc from stripe phase to isotropic stripe phase. This allows us to determine phase transition points for different values of exchange and dipole-dipole interaction ratio η = J/D and calculate the phase diagram for transitions to stripe phases AFh of different stripe width h. By using histogram method we determine the order of the transition at Tc. The first order phase transition was found to AF1 and AF2 phases and the second order one to AF3 and AF4 phases, with tricritical point being close to the AF2 and AF3 phase boundary in the phase diagram. We also calculate the structure factor above and below Tcs to AF1, AF2, AF3, and AF4 phases. Studying the dynamical properties of the model we have found that in AF1 phase and in a part of AF2 phase the spin relaxation corresponds to the Ising model dynamics. In phases AF3 and AF4 the dynamics slows down, and stripe domain growth with time is proportional to log t. With further increase of parameter η and approaching the ferromagnetic phase the dynamics satisfies the Ising model dynamics again.

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“…Here we discuss quantification of a multi-scale view of organization among metazoan individuals, which draws from roots in physical representation theory [1]. This may be useful, for example, as we explore the short-term impact of new technologies as well as the long-term window of opportunity for metazoan life [2].…”

Section: Introductionmentioning

confidence: 99%

A simplex model for layered niche networks

Fraundorf

2008

Complexity

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The standing crop of correlations in metazoan communities may be assessed by an inventory of niche structures focused inward and outward from the physical boundaries of skin (self ), gene-pool (family), and meme-pool (culture). We consider tracking the progression from three and four correlation layers in many animal communities, to five of six layers for the shared adaptation of most humans, with an attention-slice model that maps the niche-layer focus of individuals onto the 6-variable space of a 5-simplex. The measure puts questions about the effect, on culture and species, of policy and natural events into a common context, and may help explore the impact of electronically mediated codes on community health.

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Universality Away from Critical Points in Two-Dimensional Phase Transitions

Cited by 83 publications

References 24 publications

Phase transition properties of the Bell-Lavis model

Phase transition properties of the Bell-Lavis model

Modelling of thermodynamical and dynamical properties of magnetic stripes on 2D hexagonal lattice

A simplex model for layered niche networks

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