Coulomb Gas Models Research Articles

Vortex supersolid in the XY model with tunable vortex fugacity

In this paper, we investigate the XY model in the presence of an additional potential term that independently tunes the vortex fugacity favouring their nucleation. By increasing the strength of this term and thereby the vortex chemical potential µ, we observe significant changes in the phase diagram with the emergence of a normal vortex-antivortex lattice as well as a superconducting vortex-antivortex crystal (lattice supersolid) phase. We examine the transition lines between these two phases and the conventional non-crystalline one as a function of both the temperature and the chemical potential. Our findings suggest the possibility of a peculiar tricritical point where second-order, first-order, and infinite-order transition lines meet. We discuss the differences between the present phase diagram and previous results for two-dimensional Coulomb gas models. Our study provides important insights into the behaviour of the modified XY model and opens up new possibilities for investigating the underlying physics of unconventional phase transitions.

Celestial Yang-Mills amplitudes and D = 4 conformal blocks

We discuss the properties of recently constructed “single-valued” celestial four-gluon amplitudes. We show that the amplitude factorizes into the “current” part and the “scalar” part. The current factor is given by the group-dependent part of the Wess-Zumino-Witten correlator of four holomorphic currents with a non-vanishing level of Kač-Moody algebra. The scalar factor can be expressed in terms of a complex integral of the Koba-Nielsen form, similar to the integrals describing four-point correlators in Coulomb gas models and, more generally, in the infinite central charge limit of Liouville theory. The scalar part can be also obtained by a dimensional reduction of a single D = 4 conformal block and the shadow block from Minkowski space to the celestial sphere.

Coulomb gas and sine-Gordon model in arbitrary dimension

The sine-Gordon (SG), i.e. periodic scalar field theory is known to play an important role in d=2 dimensions. A paradigmatic example is the topological phase transition of the vortex dynamics in superfluid films and layered superconductors which are described by SG type models. Periodic scalar potentials find applications in d=4 dimensions, too. Higgs, inflaton and axion physics are examples where scalar fields naturally appear, thus, the SG model can be used instead of the usual polynomial one. The SG quantum field theory can be mapped onto the neutral Coulomb-gas (CG) in arbitrary dimension and the renormalization group (RG) study of the d-dimensional CG model was obtained in the dilute gas approximation. It signals a single phase for d>2, however, it was shown recently, that a suitable generalization of the SG model can posses a topological phase transitions in d=4 dimensions. Our goals in this work are (i) to map out the phase structure of the (original) SG and the equivalent neutral CG models by the functional RG method in arbitrary dimension, (ii) to compare the 3-dimensional SG and isotropic XY spin models and show that they belong to different universality classes, (iii) to study the consequences of the findings on higgs, inflaton, axion models and on the topological phase transition in higher dimensions.

Coulomb Gases Under Constraint: Some Theoretical and Numerical Results

We consider Coulomb gas models for which the empirical measure typically concentrates, when the number of particles becomes large, on an equilibrium measure minimizing an electrostatic energy. We study the behavior when the gas is conditioned on a rare event. We first show that the special case of quadratic confinement and linear constraint is exactly solvable due to a remarkable factorization, and that the conditioning has then the simple effect of shifting the cloud of particles without deformation. To address more general cases, we perform a theoretical asymptotic analysis relying on a large deviations technique known as the Gibbs conditioning principle. The technical part amounts to establishing that the conditioning ensemble is an I-continuity set of the energy. This leads to characterizing the conditioned equilibrium measure as the solution of a modified variational problem. For simplicity, we focus on linear statistics and on quadratic statistics constraints. Finally, we numerically illustrate our predictions and explore cases in which no explicit solution is known. For this, we use a Generalized Hybrid Monte Carlo algorithm for sampling from the conditioned distribution for a finite but large system.

Finite-range Coulomb gas models. I. Some analytical results.

Dyson has shown an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. In this paper, we introduce finite-range Coulomb gas models as a generalization of the Dyson models with a finite range of eigenvalue interactions. As the range of interaction increases, there is a transition from Poisson statistics to classical random matrix statistics. These models yield distinct universality classes of random matrix ensembles. They also provide a theoretical framework to study banded random matrices, and dynamical systems the matrix representation of which can be written in the form of banded matrices.

Finite-range Coulomb gas models. II. Applications to quantum kicked rotors and banded random matrices.

In part I of this two-stage exposition [Pandey, Kumar, and Puri, preceding paper, Phys. Rev. E 101, 022217 (2020)10.1103/PhysRevE.101.022217], we introduced finite-range Coulomb gas (FRCG) models, and developed an integral-equation framework for their study. We obtained exact analytical results for d=0,1,2, where d denotes the range of eigenvalue interaction. We found that the integral-equation framework was not analytically tractable for higher values of d. In this paper, we develop a Monte Carlo (MC) technique to study FRCG models. Our MC simulations provide a solution of FRCG models for arbitrary d. We show that, as d increases, there is a transition from Poisson to Wigner-Dyson classical random matrix statistics. Thus FRCG models provide a route for transition from Poisson to Wigner-Dyson statistics. The analytical formulation obtained in part I, and MC techniques developed in this paper, are used to study banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter α, the appropriate FRCG model has range d=b^{2}/N=α^{2}/N, for N→∞. Here, N is the dimensionality of the matrix in the BRM, and the evolution operator matrix in the QKR.

Finite-range Coulomb gas models of banded random matrices and quantum kicked rotors

Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte Carlo simulations. These models yield new universality classes, and provide a theoretical framework for the study of banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter α, the appropriate FRCG model has the effective range d=b^{2}/N=α^{2}/N, for large N matrix dimensionality. As d increases, there is a transition from Poisson to classical random matrix statistics.

Anomalous Wien Effects in Supercooled Ionic Liquids.

We have measured conductivity spectra of several supercooled monocationic and dicationic ionic liquids in the nonlinear regime by applying ac electric fields with large amplitudes up to about 180 kV/cm. Thereby, higher harmonic ac currents up to the 7th order were detected. Our results point to the existence of anomalous Wien effects in supercooled ionic liquids. Most ionic liquids studied here exhibit a conductivity-viscosity relation, which is close to the predictions of the Nernst-Einstein and Stokes-Einstein equations, as observed for classical strong electrolytes like KCl. These "strong" ionic liquids show a much stronger nonlinearity of the conductivity than classical strong electrolytes. On the other hand, the conductivity-viscosity relation of the ionic liquid [P_{6,6,6,14}][Cl] points to ion association effects. This "weak" ionic liquid shows a strength of the nonlinear effect, which is comparable to classical weak electrolytes. However, the nonlinearity increases quadratically with the field. We suggest that a theory for explaining these anomalies will have to go beyond the level of Coulomb lattice gas models.

Fermionic construction of tau functions and random processes

Tau functions expressed as fermionic expectation values [E. Date, M. Jimbo, M. Kashiwara, T. Miwa, Transformation groups for soliton equations, in: M. Jimbo, T. Miwa (Eds.), Nonlinear Integrable Systems—Classical Theory and Quantum Theory, World Scientific, 1983, pp. 39–120] are shown to provide a natural and straightforward description of a number of random processes and statistical models involving hard core configurations of identical particles on the integer lattice, like a discrete version simple exclusion processes (ASEP), nonintersecting random walkers, lattice Coulomb gas models and others, as well as providing a powerful tool for combinatorial calculations involving paths between pairs of partitions. We study the decay of the initial step function within the discrete ASEP (d-ASEP) model as an example. For constant hopping rates we obtain Vershik–Kerov type of asymptotic configuration of particles.

Nature of the deconfining phase transition in the (2+1)-dimensional SU(N) Georgi–Glashow model

Abstract The nature of the deconfining phase transition in the ( 2 + 1 )-dimensional SU( N ) Georgi–Glashow model is investigated. Within the dimensional-reduction hypothesis, the properties of the transition are described by a two-dimensional vectorial Coulomb gas models of electric and magnetic charges. The resulting critical properties are governed by a generalized SU( N ) sine-Gordon model with self-dual symmetry. We show that this model displays a massless flow to an infrared fixed point which corresponds to the Z N parafermions conformal field theory. This result, in turn, supports the conjecture of Kogan, Tekin, and Kovner that the deconfining transition in the ( 2 + 1 )-dimensional SU( N ) Georgi–Glashow model belongs to the Z N universality class.

Classification of conformal field theories based on Coulomb gases. Application to loop models

We present a method for classifying conformal field theories based on Coulomb gases (bosonic free-field construction). Given a particular geometric configuration of the screening charges, we give necessary conditions for the existence of degenerate representations and for the closure of the vertex-operator algebra. The resulting classification contains, but is more general than, the standard one based on classical Lie algebras. We then apply the method to the Coulomb gas theory for the two-flavoured loop model of Jacobsen and Kondev. The purpose of the study is to clarify the relation between Coulomb gas models and conformal field theories with extended symmetries.

Origin of logarithmic operators in conformal field theories

We study logarithmic operators in Coulomb gas models, and show that they occur when the “puncture” operator of the Liouville theory is included in the model. We also consider WZNW models for SL(2, R), and for SU(2) at level 0, in which we find logarithmic operators which form Jordan blocks for the current as well as the Virasoro algebra.

Ising transition in the classical ANNNXY model

We investigate the XY model with ferromagnetic nearest and antiferromagnetic next-to-nearest neighbours couplings (ANNNXY model). We formulate the study of both phases of the model in terms of different Coulomb gas models. The non-frustrated ferromagnetic phase is thus transformed into a usual Coulomb gas with one species, whereas the frustrated phase is translated into a Coulomb gas with three species interacting with each other in an anisotropic lattice. We then generalize the Kosterlitz - Thouless renormalization group equations for both phases by treating the Ising and Kosterlitz - Thouless order parameters in an independent way. This enables us to discuss the nature of the transition (Ising and (or) Kosterlitz - Thouless) in the frustrated phase.

Relaxation of charged particles in disordered systems

Dynamic properties of Coulomb lattice gas models obtained from Monte Carlo simulation are briefly summarized. The utility of such models in describing the relaxational behaviour of complex ionic systems is pointed out. New simulations of conductivity spectra and nuclear spin relaxation are presented for the counterion model, where ions are diffusing in the presence of long-range Coulomb fields due to randomly placed charge-compensating centers. The results are discussed in comparison with experiments on ion-conducting glasses.

Critical behavior and duality in extended sine-Gordon theories

We study the critical properties of vectorial sine-Gordon theories based on the root system of simply-laced Lie algebras. We introduce the dual operators and study the renormalization aspects of these theories. These models are identified with vectorial Coulomb gas models of electric and magnetic charges and generalized Toda field theories. We prove that these theories are consistently renormalizable for simply-laced Lie algebras, but non-renormalizable in general in the non-simply-laced case. These models provide a description for the statistical mechanics of melting in the SU(3) case. They also provide a simplified model for strings compactified on root lattices. We compute the RG beta functions to quadratic order for general simply-laced algebras and find that in general there is a Weyl singlet, self-dual fixed point. This fixed point describes a critical theory with condensates of electric and magnetic charges corresponding to tachyonic and winding modes in string language. The different phases are related by Weyl and duality symmetry. The phase structure is conjectured in the general case, and analyzed in detail for SU(3) and SO(6). We compute Zamolodchikov's c-function to cubic order in the couplings in the general case and the conformal anomaly at the self-dual fixed point for SU( N).

BRST approach to minimal models

We introduce a BRST charge in a series of Coulomb gas models in two dimensions. We show that these models, once restricted to BRST states, are equivalent to the minimal two-dimensional conformal invariant models of Belavin, Polyakov and Zamolodchikov. Primary chiral fields are identified with BRST invariant vertex operators with screening charges. These operators are non-vanishing if and only if the “fusion rules” are fulfilled. As an application, we prove a Feigin-Fuks integral representation for generaln-point functions on the plane and on the torus.

Scaling equations for the one-dimensional two-fermion model

The equivalence of the one-dimensional two-fermion model, on one hand, with the two-dimensional Coulomb gas and sine-Gordon models on the other is worked out by employing the Jordan boson representation and the point-splitting regularization. The distinction is made throughout between the bandwidth cut-off and momentum-transfer cut-off. It is shown that the coupling constants, both in the weak-coupling regime and near the Luther-Emery exact solution, scale with the momentum-transfer cut-off. The relationship between the bosonized form of the two-fermion model and the corresponding Fermi gas model is briefly discussed.

The Kosterlitz-Thouless transitions by the mayer expansion finiteness of the perturbations

The Kosterlitz-Thouless transitions in 2D XY and Coulomb gas models are discussed by the Mayer expansion. After transforming the 2D XY model into a (generalzed) 2D Coulomb gas model by the duality transformation, it is shown that the free energy (pressure) and the two point correlation function 〈cos( θ 0− θ ζ )〉 are expressed as Σa N ( β) and exp[( 2 β ) C 0(ζ) + Σb N(β:ζ)] , respectively, for large inverse temperature β > β c , where { a N ( β)} are the usual virial coefficients and { a N , b N } are the contributions from N-electron system. Moreover C 0( ζ) ≅ − (2 π) −1 log(| ζ| + 1), | a N ( β)| ≤ C 1( N) exp[− βK 3 N] and | b N ( β: N) ≤ C 2( N) exp[− βK 4 N] | C 0( ζ)| ( K i > 0). By comparing this system with the dipole gas system in which these series converge absolutely, it is conjectured that these series converge absolutely for large β.