[N]pT Monte Carlo Simulations of the Cluster-Crystal-Forming Penetrable Sphere Model

Certain models with purely repulsive pair interactions can form cluster crystals with multiply-occupied lattice sites. Simulating these models' equilibrium properties is, however, quite challenging. Here, we develop an expanded isothermal-isobaric $[N]pT$ ensemble that surmounts this problem by allowing both particle number and lattice spacing to fluctuate. We apply the method with a Monte Carlo simulation scheme to solve the phase diagram of a prototypical cluster-crystal former, the penetrable sphere model (PSM), and compare the results with earlier theoretical predictions. At high temperatures and densities, the equilibrium occupancy $n_{\mathrm{c}}^{\mathrm{eq}}$ of face-centered cubic (FCC) crystal increases linearly. At low temperatures, although $n_{\mathrm{c}}^{\mathrm{eq}}$ plateaus at integer values, the crystal behavior changes continuously with density. The previously ambiguous crossover around $T\sim0.1$ is resolved

Sine-Gordon/Coulomb Gas Soliton Correlation Functions and an Exact Evaluation of the Kosterlitz-Thouless Critical Exponent

We present an exact derivation for the asymptotic large distance behavior of the spin two-point correlation function in the XY-model. This allows for the exact obtainment of the critical exponent $\eta=1/4$ at the Kosterlitz-Thouless transition that occurs in this model and in the 2D neutral Coulomb gas and which has been previously obtained by scaling arguments. In order to do that, we use the language of sine-Gordon theory to obtain a Coulomb Gas description of the XY-model spin correlation function, which becomes identified with the soliton correlator of that theory. Using a representation in terms of bipolar coordinates we obtain an exact expression for the asymptotic large distance behavior of the relevant correlator at $\beta^2=8\pi$, which corresponds to the Kosterlitz-Thouless transition. The result is obtained by approaching this point from the plasma (high-temperature) phase of the gas. The vortex correlator of the XY-model is also obtained using the same procedure.Comment: To appear in J. Stat. Phys., 11 page

Exact Asymptotic Behaviour of Fermion Correlation Functions in the Massive Thirring Model

We obtain an exact asymptotic expression for the two-point fermion correlation functions in the massive Thirring model (MTM) and show that, for $\beta^2=8\pi$, they reproduce the exactly known corresponding functions of the massless theory, explicitly confirming the irrelevance of the mass term at this point. This result is obtained by using the Coulomb gas representation of the fermionic MTM correlators in the bipolar coordinate system.Comment: To appear in J. Phys. A: Math. Gen. 12 page

Pocket Monte Carlo algorithm for classical doped dimer models

We study the correlations of classical hardcore dimer models doped with monomers by Monte Carlo simulation. We introduce an efficient cluster algorithm, which is applicable in any dimension, for different lattices and arbitrary doping. We use this algorithm for the dimer model on the square lattice, where a finite density of monomers destroys the critical confinement of the two-monomer problem. The monomers form a two-component plasma located in its high-temperature phase, with the Coulomb interaction screened at finite densities. On the triangular lattice, a single pair of monomers is not confined. The monomer correlations are extremely short-ranged and hardly change with doping.Comment: 6 pages, REVTeX

Surface correlations for two-dimensional Coulomb fluids in a disc

After a brief review of previous work, two exactly solvable two-dimensional models of a finite Coulomb fluid in a disc are studied. The charge correlation function near the boundary circle is computed. When the disc radius is large compared to the bulk correlation length, a correlation function of the surface charge density can be defined. It is checked, on the solvable models, that this correlation function does have the generic long-range behaviour, decaying as the inverse square distance, predicted by macroscopic electrostatics. In the case of a two-component plasma (Coulomb fluid made of two species of particles of opposite charges), the density correlation function on the boundary circle itself is conjectured to have a temperature-independent behaviour, decaying as the -4 power of the distance.Comment: 15 pages, Latex, submitted to J.Phys.:Condens.Matte

High--order connected moments expansion for the Rabi Hamiltonian

We analyze the convergence properties of the connected moments expansion (CMX) for the Rabi Hamiltonian. To this end we calculate the moments and connected moments of the Hamiltonian operator to a sufficiently large order. Our large--order results suggest that the CMX is not reliable for most practical purposes because the expansion exhibits considerable oscillations.Comment: 12 pages, 5 figures, 1 tabl

Effective diffusion constant in a two dimensional medium of charged point scatterers

We obtain exact results for the effective diffusion constant of a two dimensional Langevin tracer particle in the force field generated by charged point scatterers with quenched positions. We show that if the point scatterers have a screened Coulomb (Yukawa) potential and are uniformly and independently distributed then the effective diffusion constant obeys the Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained for pure Coulomb scatterers frozen in an equilibrium configuration of the same temperature as that of the tracer.Comment: 9 pages IOP LaTex, no figure

The statistical mechanics of the classical two-dimensional Coulomb gas is exactly solved

The model under consideration is a classical 2D Coulomb gas of pointlike positive and negative unit charges, interacting via a logarithmic potential. In the whole stability range of temperatures, the equilibrium statistical mechanics of this fluid is exactly solvable via an equivalence with the integrable 2D sine-Gordon field theory. The exact solution includes the bulk thermodynamics, special cases of the surface thermodynamics, and the large-distance asymptotic behavior of the two-body correlation functions.Comment: Talk presented at the SCCS02 meeting in Santa Fe, to appear in J.Phys. A: Math. Ge