Tricritical universality in a two-dimensional spin fluid

Wilding, Nigel B.; Nielaba, Peter

doi:10.1103/physreve.53.926

Cited by 105 publications

(121 citation statements)

References 39 publications

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“…Earlier finite-size studies that explores the conformal invariance of this model were done in its τ -continuum formulation [9,10]. In figure 1 (5) for lattice sizes up to N = 10), in agreement with previous Monte Carlo [7] and finite-size calculations [8].…”

Section: The Spin-1 Modelsupporting

confidence: 72%

“…In order to compare our estimate for the tricritical point with the previous results we have also calculated the conformal anomaly and scaling dimensions by using the tricritical point estimated in Refs. [7,8]. These results show us that the extrapolated values of the conformal anomaly is similar to ours, however our estimate for the scaling dimensions are much better than the values obtained at their estimated tricritical point.…”

Section: The Spin-1 Modelmentioning

confidence: 28%

“…In the critical regions of the phase transition line (continuum curve) the conformal anomaly and the scaling dimensions can be calculated exploring the conformal invariant relations (6) and (7). From Eq.…”

Section: The Spin-1 Modelmentioning

confidence: 99%

“…In the case where S = 1 this Hamiltonian was proposed originally by Blume and Capel [1] for treating magnetic systems and has also been used in describing 3 He-4 He mixtures [2]. This S = 1 model was studied by a variety of methods such as mean field [1], two-spin cluster [3], variational methods [4], constant coupling approximation [5], Monte Carlo simulations [6,7], finite-size-scaling on its transfer matrix [8] or quantum Hamiltonian [9,10] and renormalization group methods [11,12]. It is well established that for dimension d ≥ 2 the S = 1 model presents a phase diagram with ordered ferromagnetic and disordered paramagnetic phases separated by a transition line which changes from a second-order character (Ising type) to a first-order one at a tricritical point.…”

Section: Introductionmentioning

confidence: 99%

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Critical behavior of the spin-32Blume-Capel model in two dimensions

et al. 1998

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The phase diagram of the spin-3/2 Blume-Capel model in two dimensions is explored by conventional finite-size scaling, conformal invariance and Monte Carlo simulations. The model in its τ -continuum Hamiltonian version is also considered and compared with others spin-3/2 quantum chains. Our results indicate that differently from the standard spin-1 Blume-Capel model there is no multicritical point along the order-disorder transition line. This is in qualitative agreement with mean field prediction but in disagreement with previous approximate renormalization group calculations.

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Section: The Spin-1 Modelsupporting

confidence: 72%

Section: The Spin-1 Modelmentioning

confidence: 28%

Section: The Spin-1 Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Critical behavior of the spin-32Blume-Capel model in two dimensions

et al. 1998

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“…At the TCP the critical line meets the first order transition line (long dashed line). We did not calculate the TCP because its position is known with quite a high accuracy from PR [27] (1 /K t = 0.610(5), D t = 1.965(5)) and MC results obtained by Wilding at al [29] (1 /K t = 0.608(1), D t = 1.9665(3)) -not shown in Fig. 6.…”

Section: Resultsmentioning

confidence: 99%

Simulations of Critical Properties of Classical Spin Models

Kozłowski¹,

Pawlicki²,

Kamieniarz³

1997

CMST

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Two methods of simulations are described: an exact one -transfer matrix technique and a statistical one -Monte Carlo method. Both of them are applied to investigate critical properties of classical spin models. To do this we also exploit finite size scaling and the critical point ratio of the square of the second moment of the order parameter to its fourth moment. General definition of a classical spin model as well as particular definitions of models are presented. Results of both methods are in good agreement and, moreover, they are consistent with numerical results provided by literature. 1Classical spin models A spin is a quantity hard to understand on the grounds of classical physics. A notion of a spin comes from experimental results and as a physical quantity it is described by a spin operator in the formalism of quantum mechanics. As yet only in this formalism a definition of a spin is reasonable. Thus, when we talk about spin in the context of classical models we do not mean a quantum spin operator. A name "spin" is used to call a set of numbers labeling states of an atom or a molecule, or in general, a site of a lattice. The name comes from the fact that these numbers are eigenvalues of the z component of a real quantum spin operator. So, defining a quantum model (e.g. of a solid located at each site i of a lattice, but when we define a classical spin model we use variables S i located at each site i of a lattice, where S i is an eigenvalue of a z component of an operator Classical spin models may be sometimes regarded as approximation of quantum spin models, but not always. Sometimes a spin variable is used to write 39 state) we use operators

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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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Tricritical universality in a two-dimensional spin fluid

Cited by 105 publications

References 39 publications

Critical behavior of the spin-32Blume-Capel model in two dimensions

Critical behavior of the spin-32Blume-Capel model in two dimensions

Simulations of Critical Properties of Classical Spin Models

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

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