Exact results for correlations in a two-component log-gas

A study of the one-dimensional lattice gas of positive and negative charges interacting via the logarithmic potential is continued. The two-particle distribution functions are evaluated exactly at the couplings=2 and 4. It is proved that the=4 isotherm exhibits an insulator-conductor phase transition at the reduced density 1/2, and the scaling behavior of the correlations near this critical point is given. Similarities of the conjectured phase diagram with that of a one-dimensional one-component log-gas in a periodic potential are noted.     

Charged rods in a periodic background: A solvable model

The one-component Coulomb system with logarithmic potential in a periodic background is considered. In one dimension, when the background has the same period as the average interparticle spacing, the system is exactly solvable for three values of the coupling constant. The exact solution exhibits insulating-conducting phase transitions. An heuristic argument is presented which predicts the phase diagram for this system.     

Solvable isotherms for a two-component system of charged rods on a line

The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constant=q ²/k _B T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity plane, all the zeros of the grand partition function lie on the negative real axis for<2, on the point=–1 for=2, and on the unit circle for>2. In addition, for>4, we conjecture in general and prove at=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2.     

Monte carlo simulations of the two-dimensional two-component plasma on a line

We study by means of Monte Carlo simulations the Kosterlitz-Thouless transition for the two-dimensional, two-component plasma confined on a line.     

The two-dimensional one-component plasma in a doubly periodic background: Exact results

We revisit the equilibrium classical statistical mechanics of the two-dimensional one-component plasma, for the special value =2 of the coupling constant. Using a new method, we find that the model is solvable (then-body densities can be explicitly computed) for a larger class of inhomogeneous backgrounds. In particular, we can deal with a doubly periodic background; this is a classical model for a crystal made of fixed ions and mobile electrons. At =2, this system is conducting: the correlations have a fast decay, and the Stillinger-Lovett screening sum rule is obeyed.     

Classical Coulomb fluids in a confined geometry

It has already been argued that a classical (three-dimensional) Coulomb fluid confined between two parallel walls exhibits ideal gas features when the distance between the walls becomes small; this is confirmed in the present paper. Two-dimensional models of Coulomb fluids (with a logarithmic interaction), confined in a strip, are also studied. These models do not become ideal gases in the narrow strip limit. The correlation functions are also studied. There is a special temperature at which exact results are obtained. At that temperature, the two-dimensional, two-component plasma (two-dimensional Coulomb gas), which is a conductor when unconfined, becomes a dielectric as soon as it is confined in a strip of noninfinite width. This can be understood as a displacement of the Kosterlitz-Thouless transition by the confinement.     

A new rigorous upper bound for the inverse critical temperature of the two-dimensional Coulomb gas

In this paper we show how to improve the recent result _c 17.2 on the inverse critical temperature for the two-dimensional Coulomb gas at low density to get the following upper bound: _c 16.     

Exact results for a generalized classicalO(n) matrix spin model

A generalizedO(n) matrix version of the classical Heisenberg model, introduced by Fuller and Lenard as a classical limit of a quantum model, is solved exactly in one dimension. The free energy is analytic and the pair correlation functions decay exponentially for all finite temperatures. It is shown, however, that even for a finite number of spins the model has a phase transition in then limit. The transition features a specific heat jump, zero long-range order at all temperatures, and zero correlation length at the critical point. The Curie-Weiss version of the model is also solved exactly and shown to have standard mean-field type behavior for all finiten and to differ from the one-dimensional results in then limit.     

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.     

二维情况下两组分带电囊泡形变耦合相分离的理论模拟研究

结合离散空间变分方法和耗散动力学研究了二维两组分带电囊泡的形变耦合相分离,系统地考察了囊泡带电量组分含量、带电组分的电荷密度、两组分间的相容性和温度等因素对形变耦合相分离动力学的影响.模拟结果表明电荷引入可增加不同组分间的表观相溶性.当温度较高时,静电相互作用可直接抑制囊泡相分离,避免了同种组分的团聚;当温度较低时,静电相互作用则可明显增加分相相区数目,使其呈微观相分离,从而避免了同种组分大范围的团聚.     

Heavy ions at the LHC: Physics perspectives and experimental program

Ultrarelativisitc heavy ion physics is entering the new era of collider experiments with the start-up of RHIC at BNL and construction for detectors at LHC well under way. At this cross-roads, the article will give a summary of the experimental program and our current view of heavy ion physics at the LHC, concentrating in particular on physics topics that are different or unique compared to current facilities.     

Exact results for a dilute Potts model

Exact results are obtained for the annealed, dilute,q-component Potts model on the decorated square lattice. The phase diagram is found to consist of a high-temperature region, a low-temperature region, and a two-phase region in between which arises only forq>4: exact expressions for the phase boundary and the critical probability are derived. At the critical point the specific heat is generally finite and has a cusp; the slope of the cusp is finite forq=4 and infinite (vertical) forq=2 and 3.Work supported in part by NSF Grant No. DMR 78-18808.     

Dynamical Phase Transition in a Neural Network Model with Noise: An Exact Solution

The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same value. It is shown that, under very general conditions, there exists a critical value _c of the noise, below which the network remains organized and above which it behaves randomly. The existence and nature of the phase transition are computed analytically, showing that the critical exponent is 1/2. The dependence of _c on the parameters of the network is obtained. These results are then compared with two numerical realizations of the network.     

The interfacial surface tension of a quark-gluon plasma fireball in a hadronic medium

We calculate the interfacial surface tension of a QGP-fireball in a hadronic medium in the Ramanathan et al statistical model. The constancy of the ratio of the surface tension with the cube of the critical transition temperature is in overall accordance with lattice QCD findings. It is in complete agreement with a recent MIT bag model calculation of surface tension. The velocity of sound in the QGP droplet is predicted to be in the range (0.27 ± 0.02) times the velocity of light in vacuum and this value is independent of both the value of the transition temperature and the model parameters.      

Bifurcation of a periodic instanton and quantum－classical transition in the biaxial nano－ferromagnet with a magnetic field along hard axis

Crossover from classical to quantum regimes of the barrier transition rate in a biaxial ferromagnetic magnet with a magnetic field applied along hard anisotropy axis is investigated. We show that the type of action-temperature diagrams can he determined by counting the number of bifurcation points. The model possesses not only the known type I and Ⅱ, hut also the interesting type Ⅲ and Ⅳ of transition which do not occur in general.     

A Generalized Geometric Measurement of Quantum Discord:Exact Treatment

A generalization of the geometric measure of quantum discord is introduced in this article, based on Hellinger distance. Our definition has virtues of computability and independence of local measurement. In addition it also does not suffer from the recently raised critiques about quantum discord. The exact result can be obtained for bipartite pure states with arbitrary levels, which is completely determined by the Schmidt decomposition. For bipartite mixed states the exact result can also be found for a special case. Furthermore the generalization into multipartite case is direct. It is shown that it can be evaluated exactly when the measured state is invariant under permutation or translation. In addition the detection of quantum phase transition is also discussed for Lipkin–Meshkov–Glick and Dicke model.     

Exact results for a meniscus in a three-phase system within an SOS-type approximation

The shape of a meniscus of one phase between two others is studied in two dimensions using random walk models. An interface with a meniscus is approximated by two random walks forming microscopic droplets of the intruding phase before and after a macroscopic lens. Within this class of models, we establish a Wulff construction and prove the Herring relations between contact angles. We give explicit formulas for the contact angles as functions of temperature, both at low temperatures and near the wetting transition.     

Phase transitions in hadronic systems and thermodynamics of a system with an exponential spectrum

Both nuclear matter and hadronic matter at high excitations can be described by a liquid-vapor phase transition. For the hadronic systems, a system with an exponential mass spectrum (Hagedorn-like or bag-like) leads to a thermodynamics which is identical to that of a two phase coexistence at a fixed temperature.     

Structure and phase transition of a two—dimensional dusty plasma

The structure and phase transition of a two-dimensional (2D) dusty plasma have been investigated in detail bymolecular dynamics simulation. Pair correlation function, static structure factor, mean square displacement, and bondangle correlation function have been calculated to characterize the structural properties. The variation of internalenergy, shear modulus, particle trajectories and structural properties with temperature has been monitored to studythe phase transition of the 2D dusty plasma system. The simulation results are in favour of a two-step continuoustransition for this kind of plasma.     

Exact Determination of the Phase Structure of a Multi-Species Asymmetric Exclusion Process

We consider a multi-species generalization of the Asymmetric Simple Exclusion Process on an open chain, in which particles hop with their characteristic hopping rates and fast particles can overtake slow ones. The number of species is arbitrary and the hopping rates can be selected from a discrete or continuous distribution. We determine exactly the phase structure of this model and show how the phase diagram of the 1-species ASEP is modified. Depending on the distribution of hopping rates, the system can exist in a three-phase regime or a two-phase regime. In the three-phase regime the phase structure is almost the same as in the one species case, that is, there are the low density, the high density and the maximal current phases, while in the two-phase regime there is no high-density phase.