Critical line near the zero-density critical point of the Kosterlitz-Thouless transition

Using low-fugacity expansions, we study the exact behavior of the Kosterlitz-Thouless critical line near the zero-density critical point. We show that the critical temperature deviates from its zero-density value by a term proportional to the square root of the density.     

Pseudo-Hamiltonians for the Potts model at the critical point

The diagonal transfer matrix of the 2-dimensional, q-component Potts model on a square lattice is shown to commute with a linear operator at the critical point. In the 4-component model the linear operator is equivalent to the linear Heisenberg chain.     

The soft-sphere model for metals near the critical point

Abstract

The soft-sphere model is convenient and accurate for predicting fluid phase thermodynamics. The validity of the model for describing the equation-of-state derivatives, Grüneisen's gamma and sound velocity, is shown.     

On the Heisenberg model in the paramagnetic region and at the critical point

Zeitschrift für Physik A Hadrons and nuclei - An exact diagram technique suitable especially for calculating the time dependent correlation functions in the Heisenberg model is given. We apply...     

Droplet model for sound absorption in fluids near the critical point

The dynamic droplet model of critical fluids is applied to understanding critical fluid sound absorption. The resonance frequency of an oscillating droplet is used to explain the scaling on frequency and temperature observed in sound absorption data.     

On the water-induced critical double point in a polymer solution: the role of isotopic substitution

This paper examines the effect of substitution of water by heavy water in a polymer solution of polystyrene (molecular weight=13000) and acetone. A critical double point (CDP), at which the upper and the lower partially-miscible regions merge, occurs at nearly the same coordinates as for the system [polystyrene+acetone+water]. The shape of the critical line for [polystyrene+acetone+heavy water] is highly asymmetric. An explanation for the occurrence of the water-induced CDP in [polystyrene+acetone] is advanced in terms of the interplay between contact energy dissimilarity and free-volume disparity of the polymer and the solvent. The question of the possible existence of a one-phasehole in an hourglass phase diagram is addressed in [polystyrene+acetone+water]. Our data exclude such a possibility.     

Quantum critical end point for the Kondo volume collapse model

The Kondo volume collapse describes valence transitions in f-electron metals and is characterized by a line of first order transitions in the pressure-temperature phase plane terminated at critical end points. We analyze the quantum critical end point, when the lower end point is tuned to T=0, and determine the specific heat, thermal expansion, and compressibility. We find that the inclusion of quantum critical fluctuations leads to a novel bifurcation of the first order phase line. Finally, we show that critical strain fluctuations can cause both, superconductivity and non-Fermi liquid behavior near the critical point.     

Proximity of the superconducting dome and the quantum critical point in the two-dimensional Hubbard model

We use the dynamical cluster approximation to understand the proximity of the superconducting dome to the quantum critical point in the two-dimensional Hubbard model. In a BCS formalism, T(c) may be enhanced through an increase in the d-wave pairing interaction (V(d)) or the bare pairing susceptibility (χ(0d)). At optimal doping, where V(d) is revealed to be featureless, we find a power-law behavior of χ(0d)(ω=0), replacing the BCS log, and strongly enhanced T(c). We suggest experiments to verify our predictions.     

On the liquid-vapour-like critical point in the model of the rare earth iron garnet

The transition between two canted phases in YbIG atH 100 is examined in the framework of the model with one saturated Fe-sublattice and six sublattices of mutually independent Yb ions. In particular, the equations determining the continuous transition point and the coexistence line of these canted phases are derived. The existence of a zero frequency mode in this second order transition point is clear from this analysis, too. The analogy with the classical theory of the liquid-vapour-like phase transition, as well as the limits of the mean field approach are discussed.     

Phase diagram,correlations,and quantum critical point in the periodic Anderson model

Periodic Anderson model is one of the most important models in the field of strongly correlated electrons. With the recent developed numerical method density matrix embedding theory, we study the ground state properties of the periodic Anderson model on a two-dimensional square lattice. We systematically investigate the phase diagram away from half filling. We find three different phases in this region, which are distinguished by the local moment and the spin–spin correlation functions. The phase transition between the two antiferromagnetic phases is of first order. It is the so-called Lifshitz transition accompanied by a reconstruction of the Fermi surface. As the filling is close to half filling, there is no difference between the two antiferromagnetic phases. From the results of the spin–spin correlation, we find that the Kondo singlet is formed even in the antiferromagnetic phase.     

Part I. The 2D classical Coulomb gas near the zero-density Kosterlitz-Thouless critical point: Correlations and critical line

The 2D classical Coulomb gas undergoes the famous Kosterlitz-Thouless (KT) transition between a high-temperature conducting phase and a low-temperature insulating phase. We present various studies of the correlations in the insulating phase near the zero-density critical point. First, we briefly recall the phenomenological approach of Kosterlitz and Thouless. This theory predicts that the decay of the charge correlation is entirely controlled by the bare Coulomb potential between opposite charges only renormalized by the dielectric constante. Then, we present an analysis of the low-fugacity expansions of the correlations. The particle correlations are found to decay as 1/r⁴. The large-distance decay of the charge correlation is shown to be tightly related to the behavior of l/s in the regime of interest. Systematic resummations allow one to recover the algebraic decay predicted by the heuristic KT model. This settles on a rigorous basis various assumptions of this model. In particular, the nested pair mechanism naturally arises in the resummation scheme. Finally, we describe the phase diagram of the system according to the most recent calculations which include finite-density effects.     

Infrared asymptotic freedom for the pseudoscalar Yukawa model at the critical point

We consider the pseudoscalar Yukawa model on a four dimensional Euclidean lattice. The fermions are integrated out giving an effective boson interaction. We show that for weak coupling this interaction is in the class covered by the Gawedzki-Kupiainen renormalization group analysis. It follows that one can adjust parameters so that the flow of the renormalization group is toward a free massless boson theory. This establishes the existence of the critical theory and controls its long distance behavior.     

The critical line of an asymmetric eight vertex model

Phenomenological renormalization of finite lattice data is used to locate the critical line of an asymmetric eight-vertex model. This model reduces at a special point to a loop gas on the square lattice. The critical fugacity of the loop gas is estimated to be 2.373±0.001, whereas the correlation exponent appears to be Ising-like.