Symmetry aspects of finite-temperature confinement transitions

Analytical and numerical work on confinement phase transitions in finite-temperature Abelian and non-Abelian gauge theories is reviewed. These transitions are order-disorder transitions and their critical properties (if any) can be understood from the standard theory of critical phenomena. Strong coupling, large-N, and non-perturbative lattice methods are discussed. The role of matter fields as symmetry-breaking perturbations is noted as important to the eventual unraveling of the phase structure of quantum chromodynamics.     

Effective potential convexity and finite-temperature phase transitions

We have examined some consequences of convex effective potentials for calculations of finite temperature phase transitions.     

Critical behavior at dirty surfaces

The influence of quenched surface disorder — i.e. quenched disorder that is located at the bounding surface of a macroscopic system — on the surface critical behavior of such systems is investigated. To this end a class of semi-infinite continuum models of then-vector type with random surface interactions is studied. Both the case of surface transitions at a bulk critical point as well as that of surface transitions at a bulk tricritical point is considered. General irrelevance/relevance criteria of the Harris type are derived for both short-range and long-range correlated random surface interactions. These are used to assess the stability of the pure system critical behavior and to point out when random surface field or enhancement disorder is expected to be relevant.     

Manifestation of critical behavior at first-order phase transitions

We present in this Letter further results which are in good agreement with our earlier observations on the critical behavior at a strong first-order phase transition. More elaborate data analysis has been used here. A quantitative measure of the strength of the transition within the context of Landau theory is also given.     

Critical behaviour at the displacive limit of structural phase transitions

For a special critical point at zero temperature,T _c =0, which is called the displacive limit of a classical or of a quantum-mechanical model showing displacive phase transitions, we derive a set of static critical exponents in the large-n limit. Due to zero-point motions and quantum fluctuations at low temperatures, the exponents of the quantum model are different from those of the classical model. Moreover, we report results on scaling functions, corrections to scaling, and logarithmic factors which appear ford=2 in the classical case and ford=3 in the quantum-mechanical case. Zero-point motions cause a decrease of the critical temperature of the quantum model with respect to the classicalT _c , which implies a difference between the classical and the quantum displacive limit. However, finite critical temperatures are found in both cases ford>2, while critical fluctuations still occur atT _c =0 for 0<d≦2 in the classical case and for 1 <d≦2 in the quantum model. Further we derive the slope of the critical curve at the classical displacive limit exactly. The absence of 1/n-corrections to the exponents of the classical model is also discussed.     

Partial order and finite-temperature phase transitions in Potts models on irregular lattices

We evaluate the thermodynamic properties of the 4-state antiferromagnetic Potts model on the Union-Jack lattice using tensor-based numerical methods. We present strong evidence for a previously unknown, "entropy-driven," finite-temperature phase transition to a partially ordered state. From the thermodynamics of Potts models on the diced and centered diced lattices, we propose that finite-temperature transitions and partially ordered states are ubiquitous on irregular lattices.     

Reemergent metal-insulator transitions in manganites exposed with spatial confinement

The metal-insulator transition is characterized as a single peak in the temperature-dependent resistivity measurements; exceptions to this have never been seen in any single crystal material system. We show that by reducing a single crystal manganite thin film to a wire with a width comparable to the mesoscopic phase-separated domains inherent in the material, a second and robust metal-insulator transition peak appears in the resistivity versus temperature measurement. This new observation suggests that spatial confinement is a promising route for the discovery of emergent physical phenomena in complex oxides.     

Critical behavior and 1/f noise in lumped systems undergoing two phase transitions

It is shown that the interaction of order parameters when subcritical and supercritical phase transitions take place simultaneously may result in a self-organized critical state and cause a 1/f ^α fluctuation spectrum, where 1≤α≤2. Such behavior is inherent in potential and nonpotential systems of nonlinear Langevin equations. A numerical analysis of the solutions to the proposed systems of stochastic differential equations showed that the solutions correlate with fractional integration and differentiation of white noise. The general behavior of such a system has features in common with self-organized criticality.     

Phase transitions in diluted magnets: Critical behavior,percolation, and random fields

Transition metal halides provide realizations of Ising,XY, and Heisenberg antiferromagnets in one, two, and three dimensions. The interactions, which are of short range, are generally well understood. By dilution with nonmagnetic species such as Zn⁺⁺ or Mg⁺⁺ one is able to prepare site-random alloys which correspond to random systems of particular interest in statistical mechanics. By mixing two magnetic ions such as Fe⁺⁺ and Co⁺⁺ one can produce magnetic crystals with competing interactions-either in the form of competing anisotropies or competing ferromagnetic and antiferromagnetic interactions. In this paper the results of a series of neutron scattering experiments on these systems carried out at Brookhaven over the past several years are briefly reviewed. First the critical behavior in Rb₂Mn_0.5Ni_0.5F₄ and Fe_cZn_1–cF₂ which correspond to two-dimensional and three-dimensional random Ising systems, respectively, are discussed. Percolation phenomena have been studied in Rb₂Mn_cMg_l–cF₄, Rb₂Co_cMg_l–cF₄, KMn_cZ_l-cF₃, and Mn_cZn_l–cF₂ which correspond to two-and three-dimensional Heisenberg and Ising models, respectively. In these casesc is chosen to be in the neighborhood of the nearest-neighbor percolation concentration. Application of a uniform field to the above systems generates a random staggered magnetic field; this has facilitated a systematic study of the random field problem. As we shall discuss in detail, a variety of novel, unexpected phenomena have been observed.     

The finite-temperature phase transition at infinite N

The finite-temperature breakdown of the global Z(N) symmetry of 3 + 1 dimensional lattice gauge theories is studied within the framework of a reduced, quenched, large-N model using both analytical and numerical methods.     

Critical statics of elastic phase transitions

The critical behaviour of elastic phase transitions of second order, where the order parameter is a strain component and the soft mode is an acoustic mode, is studied by the RNG method. A classification of the different types of elastic phase transitions in three-dimensional crystals is given and two general models are introduced for these transitions which are suitable for an investigation by the RNG method. Critical exponents of thesed-dimensional models with anm-dimensional subspace of soft directions are calculated by the-expansion as a function ofd andm. The critical dimensionality is shifted to lower values in comparison to spin models. In systems where softening occurs only in a one-dimensional subspace the critical behaviour is classical in three dimensions, for those where softening occurs in a two-dimensional subspace logarithmic corrections to the classical behaviour are found.Work supported by the Fonds zur Förderung der wissenschaftlichen ForschungA short account of the present work was reported (by F.S.) at the MECO-Seminar of Phase Transitions, 1976, University of Ljubljana, Yugoslavia     

Critical phenomena in nonequilibrium phase transitions

We discuss a number of models associated with phase transitions in purely kinetic models where detailed balance does not hold as in thermal equilibrium systems. These models include some of the features of heterogeneous catalysis on a surface, and are used to examine the effect of local correlations on the reaction process. We argue that many models which do not include desorption will show the same kind of critical behavior if they have a continuous transition to a poisoned state. We also present results for a model with a continuous transition to a non-poisoned state. The effect of adding desorption, diffusion, and anisotropy to these idealized models is also discussed.