Duality and Fisher zeros in the two-dimensional Potts model on a square lattice

We investigate the crossover properties of the frustrated percolation model on a two-dimensional square lattice, with asymmetric distribution of ferromagnetic and antiferromagnetic interactions. We determine the critical exponents ν, γ, and β of the percolation transition of the model, for various values of the density of antiferromagnetic interactions π in the range 0≤π≤0.5. Our data is consistent with the existence of a crossover from random percolation behavior for π=0, to frustrated percolation behavior, characterized by the critical exponents of the ferromagnetic 1/2-state Potts model, as soon as π>0.

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Фазовые переходы в двумерной слабо разбавленной пятивершинной модели Поттса

Физика твердого тела ◽

10.21883/ftt.2020.07.49478.051 ◽

2020 ◽

Vol 62 (7) ◽

pp. 1088

Author(s):

А.К. Муртазаев ◽

А.Б. Бабаев ◽

Г.Я. Атаева

Keyword(s):

Phase Transition ◽

Order Phase Transition ◽

Potts Model ◽

Square Lattice ◽

Study Phase ◽

Two Dimensional ◽

Nonmagnetic Impurities ◽

First Order Phase Transition ◽

First Order Phase ◽

Binder Cumulants

Computer simulation was used to study phase transitions in the two-dimensional weakly diluted Potts model on a square lattice at q=5. Systems with linear dimensions L×L=N, L=10-120 are considered. Based on fourth-order Binder cumulants, it was shown that the introduction of nonmagnetic impurities into the spin system described by the two-dimensional Potts model with q=5 leads to a change in the first-order phase transition to the second-order phase transition.

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Fisher zeros and singular behaviour of the two-dimensional Potts model in the thermodynamic limit

Journal of Physics A General Physics ◽

10.1088/0305-4470/31/47/004 ◽

1998 ◽

Vol 31 (47) ◽

pp. 9419-9427 ◽

Cited By ~ 6

Author(s):

R Kenna

Keyword(s):

Thermodynamic Limit ◽

Potts Model ◽

Two Dimensional ◽

Singular Behaviour ◽

Fisher Zeros

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Two‐Dimensional V‐VI Binary Nanosheets with Square Lattice: A Theoretical Investigation

physica status solidi (b) ◽

10.1002/pssb.202100178 ◽

2021 ◽

Author(s):

Xin Qiao ◽

Xiaodong Lv ◽

Yinan Dong ◽

Yanping Yang ◽

Fengyu Li

Keyword(s):

Theoretical Investigation ◽

Square Lattice ◽

Two Dimensional

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Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

Journal of High Energy Physics ◽

10.1007/jhep12(2020)019 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Yifei He ◽

Jesper Lykke Jacobsen ◽

Hubert Saleur

Keyword(s):

Potts Model ◽

Correlation Functions ◽

Liouville Theory ◽

Analytical Determination ◽

Conformal Weight ◽

Two Dimensional ◽

Conformal Blocks ◽

Conformal Bootstrap ◽

Point Correlation

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

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Structural Disorder and Collective Behavior of Two-Dimensional Magnetic Nanostructures

Nanomaterials ◽

10.3390/nano11061392 ◽

2021 ◽

Vol 11 (6) ◽

pp. 1392

Author(s):

David Gallina ◽

G. M. Pastor

Keyword(s):

Interaction Energy ◽

Time Evolution ◽

Magnetic Nanostructures ◽

Thermal Quenching ◽

Structural Disorder ◽

Square Lattice ◽

Multiple Time Scales ◽

Multiple Time ◽

Two Dimensional ◽

Energy Landscapes

Structural disorder has been shown to be responsible for profound changes of the interaction-energy landscapes and collective dynamics of two-dimensional (2D) magnetic nanostructures. Weakly-disordered 2D ensembles have a few particularly stable magnetic configurations with large basins of attraction from which the higher-energy metastable configurations are separated by only small downward barriers. In contrast, strongly-disordered ensembles have rough energy landscapes with a large number of low-energy local minima separated by relatively large energy barriers. Consequently, the former show good-structure-seeker behavior with an unhindered relaxation dynamics that is funnelled towards the global minimum, whereas the latter show a time evolution involving multiple time scales and trapping which is reminiscent of glasses. Although these general trends have been clearly established, a detailed assessment of the extent of these effects in specific nanostructure realizations remains elusive. The present study quantifies the disorder-induced changes in the interaction-energy landscape of two-dimensional dipole-coupled magnetic nanoparticles as a function of the magnetic configuration of the ensembles. Representative examples of weakly-disordered square-lattice arrangements, showing good structure-seeker behavior, and of strongly-disordered arrangements, showing spin-glass-like behavior, are considered. The topology of the kinetic networks of metastable magnetic configurations is analyzed. The consequences of disorder on the morphology of the interaction-energy landscapes are revealed by contrasting the corresponding disconnectivity graphs. The correlations between the characteristics of the energy landscapes and the Markovian dynamics of the various magnetic nanostructures are quantified by calculating the field-free relaxation time evolution after either magnetic saturation or thermal quenching and by comparing them with the corresponding averages over a large number of structural arrangements. Common trends and system-specific features are identified and discussed.

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Spin-Singlet Ground State in Two-Dimensional S=1/2 Frustrated Square Lattice: (CuCl)LaNb2O7

Journal of the Physical Society of Japan ◽

10.1143/jpsj.74.1702 ◽

2005 ◽

Vol 74 (6) ◽

pp. 1702-1705 ◽

Cited By ~ 74

Author(s):

H. Kageyama ◽

T. Kitano ◽

N. Oba ◽

M. Nishi ◽

S. Nagai ◽

...

Keyword(s):

Ground State ◽

Square Lattice ◽

Singlet Ground State ◽

Two Dimensional ◽

Spin Singlet

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THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

International Journal of Modern Physics C ◽

10.1142/s012918310400687x ◽

2004 ◽

Vol 15 (10) ◽

pp. 1425-1438 ◽

Cited By ~ 5

Author(s):

A. SOLAK ◽

B. KUTLU

Keyword(s):

Cellular Automaton ◽

Phase Boundary ◽

Critical Behavior ◽

Nearest Neighbor ◽

Finite Size ◽

Square Lattice ◽

Two Dimensional ◽

Finite Size Scaling ◽

Creutz Cellular Automaton ◽

Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

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Molecular Dynamics Simulations of Shock-Defect Interactions in Two-Dimensional Nonreactive Crystals

MRS Proceedings ◽

10.1557/proc-296-161 ◽

1992 ◽

Vol 296 ◽

Cited By ~ 2

Author(s):

Robert S. Sinkovits ◽

Lee Phillips ◽

Elaine S. Oran ◽

Jay P. Boris

Keyword(s):

Molecular Dynamics ◽

Hexagonal Lattice ◽

Square Lattice ◽

Two Dimensional ◽

Connection Machine ◽

Defect Sites ◽

Principal Axes ◽

Shock Motion ◽

Defect Interactions ◽

Dynamics Simulations

AbstractThe interactions of shocks with defects in two-dimensional square and hexagonal lattices of particles interacting through Lennard-Jones potentials are studied using molecular dynamics. In perfect lattices at zero temperature, shocks directed along one of the principal axes propagate through the crystal causing no permanent disruption. Vacancies, interstitials, and to a lesser degree, massive defects are all effective at converting directed shock motion into thermalized two-dimensional motion. Measures of lattice disruption quantitatively describe the effects of the different defects. The square lattice is unstable at nonzero temperatures, as shown by its tendency upon impact to reorganize into the lower-energy hexagonal state. This transition also occurs in the disordered region associated with the shock-defect interaction. The hexagonal lattice can be made arbitrarily stable even for shock-vacancy interactions through appropriate choice of potential parameters. In reactive crystals, these defect sites may be responsible for the onset of detonation. All calculations are performed using a program optimized for the massively parallel Connection Machine.

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