Monte Carlo study of the antiferromagnetic two-dimensional Blume-Capel model

Kimel, J.D.; Black, Steve; Carter, P.; Wang, Yung‐Li

doi:10.1103/physrevb.35.3347

Cited by 51 publications

(24 citation statements)

References 16 publications

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“…1 we present the phase diagram of the BC model for /| | 1 D J = as a function of /| | H J and B /| | k T J . The solid line indicates 2 nd order antiferromagnetic-paramagnetic phase transitions, which is in good agreement with previous results [3,4]. This boundary is obtained in the standard way by measurement of fluctuations of internal energy (specific heat) and staggered magnetization (staggered susceptibility), peaks in the above quantities are interpreted as phase transitions.…”

Section: Spanning Clusterssupporting

confidence: 90%

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Multiphase structure of finite‐temperature phase diagram of the Blume–Capel model. Wang–Landau sampling method

Pawłowski

2005

Physica Status Solidi (b)

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We investigate the density of states (DOS) in an antiferromagnetic spin-system on a square lattice described by the Blume-Capel (BC) model. We use a new and very efficient simulation method, proposed by Wang and Landau, in which we estimate very precisely DOS by sampling in the space of energy. Then we calculate the thermodynamical averages like internal energy, free energy, specific heat and entropy.The BC model exhibits multicritical behaviour such as first-or second-order transitions and tricritical points. It is known that the ground state of the model can exhibit two kinds of staggered antiferromagnetic phases: AF 1 (two interpenetrating lattices with S = -1 and S = 1) and AF 2 (S = -1 and S = 0 for H < 0; S = 1 and S = 0 for H > 0). We analyze the coexistence of such phases at finite temperatures and determine border lines between them. To understand the microscopic nature of such boundaries we present also some results obtained with the standard Monte Carlo method.

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Section: Spanning Clusterssupporting

confidence: 90%

“…In the ground state one can observe 1 st order transition from (-1, 1) antiferromagnetic phase to (0, 0) paramagnetic state for /| | 2.0 D J = . The results of Monte Carlo simulations [3][4][5][6] and analysis by very accurate numerical methods [7] indicate the tricritical point presence for /| | 1.965(5)…”

Section: Introductionmentioning

confidence: 99%

Multiphase structure of finite‐temperature phase diagram of the Blume–Capel model. Wang–Landau sampling method

Pawłowski

2005

Physica Status Solidi (b)

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“…For tricritical phenomena, the highest dimension in which non-classical behaviour can be observed is d = 2 [1]. Consequently, 2d tricritical phenomena has been the subject of a large number of previous investigations, employing a wide variety of techniques, including series expansions [2], mean-field theory [3], renormalisation group (RG) [4][5][6][7][8], transfer matrix [9][10][11][12], Monte Carlo simulations [13,14] and Monte Carlo RG methods [15][16][17]. To date, however, this interest has focused almost exclusively on lattice-based spin models such as the Blume-Capel model or the spin-1 2 next-nearest-neighbour Ising model.…”

Section: Introductionmentioning

confidence: 99%

Tricritical universality in a two-dimensional spin fluid

1996

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Monte Carlo simulations are used to investigate the tricritical point properties of a 2d spin fluid. Measurements of the scaling operator distributions are employed in conjunction with a finite-size scaling analysis to locate the tricritical point and determine the directions of the relevant scaling fields and their associated tricritical exponents. The scaling operator distributions and exponents are shown to match quantitatively those of the 2d Blume-Capel model, confirming that both models belong to the same universality class. Mean-field calculations of the tricritical point properties are also compared with the simulation measurements.Comment: 9 pages Revtex, 7 ps figures (uuencoded). Phys. Rev. E. (in press). Paper also available from http://moses.physik.uni-mainz.de/~wilding/home_wilding.htm

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“…The set of exact recursive equations (18)(19)(20)(21)(22) allows obtaining by iteration the magnetization at each site of a hierarchical lattice with n generations. Values of this local magnetization can be better analyzed through its distribution along the sites of one of the shortest bond path (geodesic) connecting the root sites of the DHL graph.…”

Section: Local Magnetization Properties: Multifractal Analysismentioning

confidence: 99%

The Blume–Capel model on hierarchical lattices: Exact local properties

Rocha-Neto

Camelo-Neto

Nogueira³

et al. 2018

Physica A: Statistical Mechanics and its Applications

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The local properties of the spin one ferromagnetic Blume-Capel model defined on hierarchical lattices with dimension two and three are obtained by a numerical recursion procedure and studied as functions of the temperature and the reduced crystal-field parameter. The magnetization and the density of sites in the configuration S = 0 state are carefully investigated at low temperature in the region of the phase diagram that presents the phenomenon of phase reentrance. Both order parameters undergo transitions from the ferromagnetic to the ordered paramagnetic phase with abrupt discontinuities that decrease along the phase boundary at low temperatures. The distribution of magnetization in a typical profile was determined on the transition line presenting a broad multifractal spectrum that narrows towards the fractal limit (single point) as the discontinuities of the order parameters grow towards a maximum. The amplitude of the order-parameter discontinuities and the narrowing of the multifractal spectra were used to delimit the low temperature interval for the possible locus of the tricritical point.

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Monte Carlo study of the antiferromagnetic two-dimensional Blume-Capel model

Cited by 51 publications

References 16 publications

Multiphase structure of finite‐temperature phase diagram of the Blume–Capel model. Wang–Landau sampling method

Multiphase structure of finite‐temperature phase diagram of the Blume–Capel model. Wang–Landau sampling method

Tricritical universality in a two-dimensional spin fluid

The Blume–Capel model on hierarchical lattices: Exact local properties

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