Higgs- and quark-inspired modifications of the finite-temperature properties of the Polyakov model

(2+1)-dimensional Georgi-Glashow model, else called the Polyakov model, is explored at nonzero temperatures and in the regime when the Higgs boson is not infinitely heavy. The finiteness of the Higgs-boson mass leads to the appearance of the upper bound on the parameter of the weak-coupling approximation, necessary to maintain the stochasticity of the Higgs vacuum. The modification of the finite-temperature behavior of the model emerging due to the introduction of massless quarks is also discussed.Comment: 4 pages, LaTeX2e, no figures, uses espcrc2.sty, submitted to Nucl. Phys. B (Proc. Suppl.

Numerical Study of a Superconducting Glass Model

An XY model with random phase shifts as a model for a superconducting glass is studied in two and three dimensions by a zero temperature domain wall renormalization group which allows one to follow the flows of both the coupling constant and the disorder strength with increasing length scale. Weak disorder is found to be marginal in two and probably irrelevant in three dimensions. For strong disorder the flow is towards a non-superconducting gauge glass fixed point in 2d and a superconducting glass in 3d. Our results are in agreement with recent analytic theory and are inconsistent with earlier predictions of a re-entrant transition to a disordered phase at very low temperature and with the loss of superconductivity for any finite amount of disorder

Probing Vortex Unbinding via Dipole Fluctuations

We develop a numerical method for detecting a vortex unbinding transition in a two-dimensional system by measuring large scale fluctuations in the total vortex dipole moment ${\vec P}$ of the system. These are characterized by a quantity $\cal F$ which measures the number of configurations in a simulation for which the either $P_x$ or $P_y$ is half the system size. It is shown that $\cal F$ tends to a non-vanishing constant for large system sizes in the unbound phase, and vanishes in the bound phase. The method is applied to the XY model both in the absence and presence of a magnetic field. In the latter case, the system size dependence of $\cal F$ suggests that there exist three distinct phases, one unbound vortex phase, a logarithmically bound phase, and a linearly bound phase.Comment: 6 pages, 2 figure

On the significance of quantum effects and interactions for the apparent universality of Bloch laws for M_s(T)

The apparent universality of Bloch's T^{3/2}-law for the temperature dependence of the spontaneous magnetization, and of generalizations thereof, is considered. It is argued that in the derivation one should not only consider the exchange interaction between the spins, but also the other interactions between them, leading to elliptical spin precession and deviations from the parabolic dispersion of magnons. Also interaction effects are important to explain the apparent universality of generalized Bloch law exponents e_B, defined by M_s(T)= M_s(0)-const. x T^{e_B}, valid in a wide temperature range T_1 < T < T_2, and for dimensionalities d = 1, 2, and 3. The above-mentioned temperature range, the 'Bloch range', lies above the quantum range, where magnetic long-range order (e.g. in d=2 dimensions) is nontrivially enforced by the additional interactions, but below the thermal critical region, where universal 'anomalous scaling dimensions' apply. In contrast, for the Bloch temperature region, the universality is only apparent, i.e. a crossover-phenomenon, and simple scaling considerations with 'normal dimensions' apply. However, due to interactions, the Bloch exponent e_B depends not only on the dimensionality d of the system, but also on the spin quantum number s (mod (1/2)) of the system, i.e. for given d the Bloch exponent e_B is different for half-integer s and for integer s.Comment: LATEX, 27 pages (including 5 eps-figures); accepted by JMM

Kosterlitz-Thouless and Manning Condensation

A comparison between the Kosterlitz-Thouless theory of metal insulator transition in a two dimensional plasma and a counterion condensation in a polyelectrolyte solution is made. It is demonstrated that, unlike some of the recent suggestions, the counterion condensation and the Kosterlitz-Thouless transition are distinct.Comment: 3 pages, uses multicol.sty, accepted to Physica

Surface properties at the Kosterlitz-Thouless transition

Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with free and mixed fixed-free boundary conditions. Using a Schwarz-Christoffel conformal mapping, we deduce the exponent eta of the order parameter correlation function and its surface equivalent eta_parallel at the Kosterlitz-Thouless transition temperature. The well known value eta(T_{KT}) = 1/4 is easily recovered even with systems of relatively small sizes, since the shape effects are encoded in the conformal mapping. The exponent associated to the surface correlations is similarly obtained eta_1(T_{KT}) ~= 0.54.Comment: LaTeX file, 7 pages, 3 eps figure

Wave-function renormalization for the Coulomb-gas in Wegner-Houghton's RG method

The RG flow for the sine-Gordon model is determined by means of the method of Wegner and Houghton in next-to-leading order of the derivative expansion. For small values of the fugacity this agrees with the well-known RG flow of the two-dimensional Coulomb-gas found in the dilute gas approximation and a systematic way of obtaining higher-order corrections to this approximation is given.Comment: 4 pages, 2 figure

Bimerons in Double Layer Quantum Hall Systems

In this paper we discuss bimeron pseudo spin textures for double layer quantum hall systems with filling factor $\nu =1$. Bimerons are excitations corresponding to bound pairs of merons and anti-merons. Bimeron solutions have already been studied at great length by other groups by minimising the microsopic Hamiltonian between microscopic trial wavefunctions. Here we calculate them by numerically solving coupled nonlinear partial differential equations arising from extremisation of the effective action for pseudospin textures. We also calculate the different contributions to the energy of our bimerons, coming from pseudospin stiffness, capacitance and coulomb interactions between the merons. Apart from augmenting earlier results, this allows us to check how good an approximation it is to think of the bimeron as a pair of rigid objects (merons) with logarithmically growing energy, and with electric charge ${1 \over 2}$. Our differential equation approach also allows us to study the dependence of the spin texture as a function of the distance between merons, and the inter layer distance. Lastly, the technical problem of solving coupled nonlinear partial differential equations, subject to the special boundary conditions of bimerons is interesting in its own right.Comment: 8 ps figures included; to be published in IJMP

Defect fugacity, Spinwave Stiffness and T_c of the 2-d Planar Rotor Model

We obtain precise values for the fugacities of vortices in the 2-d planar rotor model from Monte Carlo simulations in the sector with {\em no} vortices. The bare spinwave stiffness is also calculated and shown to have significant anharmonicity. Using these as inputs in the KT recursion relations, we predict the temperature T_c = 0.925, using linearised equations, and $T_c = 0.899 \pm >.005$ using next higher order corrections, at which vortex unbinding commences in the unconstrained system. The latter value, being in excellent agreement with all recent determinations of T_c, demonstrates that our method 1) constitutes a stringent measure of the relevance of higher order terms in KT theory and 2) can be used to obtain transition temperatures in similar systems with modest computational effort.Comment: 7 pages, 4 figure