The three-dimensional three-state Potts ferromagnet exposed to random fields: evidence for a second order transition

Using large scale Monte Carlo simulations, the ordering of the three-dimensional three state Potts ferromagnet exposed to random fields is investigated. Studies of the order parameter probability distribution and of various of its moments suggest that the order of the transition depends on the strength of the random field: i.e., the first order transition of the pure ferromagnetic model persists for weak random fields, but turns into a second order transition for a range of random fields of medium strength. For large random fields the transition seems to be first order again. In this range large domains of strongly aligned Potts spins occur already in the disordered phase and the associated slow relaxation hampers significantly the Monte Carlo study of thermodynamic equilibrium phenomena. These results are discussed in the light of current theoretical concepts. Possible applications to experiments on diluted anisotropic molecular crystals and orientational glasses are briefly mentioned.     

Finite-size effects and phase transition in the three-dimensional three-state Potts model

The three-state Potts model in three dimensions is studied by Monte Carlo and finite-size scaling techniques. Using a histogram method recently proposed by Ferrenberg and Swendsen, the finite-size dependence for the maximum of the specific heat is found to scale with the volume of the system, indicating that the phase transition is of first order. The value of the latent heat per spin and the correlation length at the transition are estimated.     

The magnetic critical exponent in the three-state three-dimensional Potts model

We perform a numerical study of the Potts model q=3 in three dimensions with nearest neighbour and next to nearest neighbour couplings by means of the finite-size renormalization group method. The analysis of the magnetic critical exponents is complementary to the one of the thermal critical exponent already presented by us and confirms our conclusions that the transition from the disordered phase to the low-temperature ordered phase is first order.     

Interfacial tension of the three-state Potts model on a square lattice at a negative fields

We calculate the interfacial tension of the three-state Potts model on a square lattice at a negative field by extending the method of Selke and Pesch, which is used in the model at zero field. The transition temperature and therefore the phase diagram of the model are determined by the vanishing of the interfacial tension.     

The approach to a second order nematic-smectic A phase transition using mixtures

Binary mixtures of compounds from the homologous series 4-n-alkoxybenzylidene-4'-n-propylaniline are used to illustrate their use in approaching a second order nematic-smectic A phase transition.     

From trees to galaxies: The Potts model on a random surface

The matrix model of random surfaces with c = ∞ has recently been solved and found to be identical to a random surface coupled to a q-states Potts model with q = ∞. The mean field-like solution exhibits a novel type of tree structure. The natural question is, down to which—if any—finite values of c and q does this behavior persist? In this work we develop, for the Potts model, an expansion in the fluctuations about the q = ∞ mean field solution. In the lowest—cubic—non-trivial order in this expansion the corrections to mean field theory can be given a nice interpretation in terms of structures (trees and “galaxies”) of spin clusters. When q drops below a finite q_c, the galaxies overwhelm the trees at all temperatures, thus suppressing mean field behavior. Thereafter the phase diagram resembles that of the Ising model, q = 2.     

Orientational order in the vicinity of a second order smectic-A to nematic phase transition

Measurements of the quadrupolar splitting of the central N¹⁴ are reported for the liquid crystal NBOA. The splitting is a measure of the orientational order parameter. At the nematic to smectic-A transition, the orientational order parameter varies continuously as a function of temperature, but with a discontinuous slope, as expected of a second order phase transition. The results are interpreted in terms of the Kobayashi-McMillan theory.     

Slowing down in the three-dimensional three-state Potts glass with nearest neighbor exchange ± J: A Monte Carlo study

,Static and dynamic properties of the Potts model on the simple cubic lattice with nearest neighbor -interaction are obtained from Monte Carlo simulations in a temperature range where full thermal equilibrium still can be achieved (). For a lattice size L = 16, in this range finite size effects are still negligible, but the data for the spin glass susceptibility agree with previous extrapolations based on finite size scaling of very small lattices. While the static properties are compatible with a zero temperature transition, they certainly do not prove it. Unlike the Ising spin glass, the decay of the time-dependent order parameter is compatible with a simple Kohlrausch function, , while a power law prefactor cannot be distinguished. The Kohlrausch exponent y ( T ) decreases from at [0pt] to at [0pt] however. The relaxation time is compatible with the exponential divergence postulated by McMillan for spin glasses at their lower critical dimension, but the exponent that can be extracted still differs significantly from the theoretical value, . Thus the present results support the conclusion that the Potts spin glass in d = 3 dimensions differs qualitatively from the Ising spin glass. Received: 8 October 1997 / Accepted: 27 November 1997     

Dynamic critical behavior of the Swendsen-Wang algorithm: The two-dimensional three-state Potts model revisited

We investigate the collapse transition of lattice trees with nearest neighbor attraction in two and three dimensions. Two methods are used: (1) A stochastic optimization process of the Robbins-Monro type, which is designed solely to locate the maximum value of the specific heat; and (2) umbrella sampling, which is designed to sample data over a wide temperature range, as well as to combat the quasiergodicity of Metropolis algorithms in the collapsed phase. We find good evidence that the transition is second order with a divergent specific heat, and that the divergence of the specific heat coincides with the metric collapse.     

The antiferromagnetic transition for the square-lattice Potts model

We solve in this paper the problem of the antiferromagnetic transition for the Q-state Potts model (defined geometrically for Q generic using the loop/cluster expansion) on the square lattice. This solution is based on the detailed analysis of the Bethe ansatz equations (which involve staggered source terms of the type “real” and “anti-string”) and on extensive numerical diagonalization of transfer matrices. It involves subtle distinctions between the loop/cluster version of the model, and the associated RSOS and (twisted) vertex models. The essential result is that the twisted vertex model on the transition line has a continuum limit described by two bosons, one which is compact and twisted, and the other which is not, with a total central charge $c=2-\frac{6}{t}$, for $\sqrt{Q}=2\cos \frac{\pi }{t}$. The non-compact boson contributes a continuum component to the spectrum of critical exponents. For Q generic, these properties are shared by the Potts model. For Q a Beraha number, i.e., $Q=4{\cos }^2\frac{\pi }{n}$ with n integer, and in particular Q integer, the continuum limit is given by a “truncation” of the two boson theory, and coincides essentially with the critical point of parafermions $Z_{n-2}$.Moreover, the vertex model, and, for Q generic, the Potts model, exhibit a first-order critical point on the transition line—that is, the antiferromagnetic critical point is not only a point where correlations decay algebraically, but is also the locus of level crossings where the derivatives of the free energy are discontinuous. In that sense, the thermal exponent of the Potts model is generically equal to $\nu =\frac{1}{2}$. Things are however profoundly different for Q a Beraha number. In this case, the antiferromagnetic transition is second order, with the thermal exponent determined by the dimension of the ${\psi }_1$ parafermion, $\nu =\frac{t-2}{2}$. As one enters the adjacent “Berker–Kadanoff” phase, the model flows, for t odd, to a minimal model of CFT with central charge $c=1-\frac{6}{(t-1)t}$, while for t even it becomes massive. This provides a physical realization of a flow conjectured long ago by Fateev and Zamolodchikov in the context of $Z_N$ integrable perturbations.Finally, though the bulk of the paper concentrates on the square-lattice model, we present arguments and numerical evidence that the antiferromagnetic transition occurs as well on other two-dimensional lattices.     

The ferromagnetic transition of iron according to a Landau-theory of phase transitions of second order

The properties of iron at its ferromagnetic transition point are described by a type of Landau-theory developed for He II. The theory includes spatial fluctuations of the spontaneous magnetisation which lead to a logarithmic singularity of the specific heat nearT _c in agreement with measurements byKraftmakher andRomashina.     

Gd(0001): A semi-infinite three-dimensional heisenberg ferromagnet with ordinary surface transition

By comparing the surface and bulk magnetization of smooth, well-ordered Gd samples, we show that the surface has an ordinary transition, i.e., a common Curie temperature for surface and bulk. A quantitative statistical analysis of the temperature dependent magnetization is presented. Critical exponents for both surface, beta(S) = 0.83+/-0.04, and bulk, beta(B) = 0.376+/-0.015, are consistent with the semi-infinite three-dimensional Heisenberg model with homogeneous exchange.     

Electrostriction in a uniaxial ferroelectric with second order phase transition

The electrostriction constant γ(m²V^?2) of a uniaxial ferroelectric with a second order phase transition has been calculated as a function of the dielectric constant (?P/?E)₀. The results have been experimentally verified on triglycine sulphate (TGS) by measuring γ and (?P/?E)₀. A sign reversal of γ above the Curie temperature is presented.     

First and second order non-equilibrium phase transition and evidence for non-extensive Tsallis statistics in Earth’s magnetosphere

In this paper strong evidence is provided for significant far from equilibrium phase transition processes in the Earth’s magnetosphere as revealed by the nonlinear analysis of in situ observations. These results constitute the solid base for the solution of the durable controversy about the chaotic or non-chaotic character of the magnetospheric dynamics. During the last two decades the concept of low dimensional chaos was supported by theoretical and experimental methods by our group in Thrace and others scientists, as an explicative paradigm of the magnetospheric dynamics including substorm processes. In parallel, the concept of self-organized criticality (SOC) and space-time intermittency was introduced as new and opposing to low dimensional chaos concepts for modeling the magnetospheric dynamics. Novel results concerning the nonlinear analysis of in situ space plasma data (magnetic-electric field, energetic particles and bulk plasma flow time series) obtained by the Geotail spacecraft presented in this paper for the first time reveal the following: (a) Coexistence of SOC and chaos states in the magnetospheric system and global phase transition from one state to the other during substorms. (b) Strong intermittent turbulent character of the magnetospheric system at the SOC or the low dimensional chaos states. (c) Clear indications for non-extensivity and q-Gaussian statistics during periods of low dimensional and chaotic dynamics of the magnetosphere. (d) Low dimensional and nonlinear space plasma dynamics in the day side magnetopause and bow shock dynamics. The dual character of the magnetospheric dynamics including low dimensional chaotic (coherent) and high dimensional turbulent states, as supported in this paper, is in agreement and verifies previous theoretical and experimental studies.     

Magnetic properties of a higher than second order superconducting phase transition

Based on the measurement of the magnetic characteristics of In−Bi, In−Tl, In−Pb, Sn−Bi and Sn−Sb superconducting alloys it was stated that the phase transition type I→ type II superconductivity is of higher than second order. Comparing the experimental data with the Lifshitz’s theory it is shown that the addition falls between the values of 0.63 and 0.77.