The influence of droplet size on line tension

Within the effective interfacial Hamiltonian approach we evaluate the excess line free energy associated with cylinder-shaped droplets sessile on a stripe-like chemical inhomogeneity of a planar substrate. In the case of short-range intermolecular forces the droplet morphology and the corresponding expression for the line tension - which includes the inhomogeneity finite width effects - are derived and discussed as functions of temperature and increasing width. The width-dependent contributions to the line tension change their structure at the stripe wetting temperature T_W1: for T<T_W1 they decay exponentially while for T>T_W1 the decay is algebraic. In addition, a geometric construction of the corresponding contact angle is carried out and its implications are discussed

Finite temperature crossovers near quantum tricritical points in metals

We present a renormalization group treatment of quantum tricriticality in metals. Applying a set of flow equations derived within the functional renormalization group framework we evaluate the correlation length in the quantum critical region of the phase diagram, extending into finite temperatures above the quantum critical or tricritical point. We calculate the finite temperature phase boundaries and analyze the crossover behavior when the system is tuned between quantum criticality and quantum tricriticality.Comment: 7 pages, 5 figure

Critical temperature and Ginzburg region near a quantum critical point in two-dimensional metals

We compute the transition temperature $T_c$ and the Ginzburg temperature $T_{\rm G}$ above $T_c$ near a quantum critical point at the boundary of an ordered phase with a broken discrete symmetry in a two-dimensional metallic electron system. Our calculation is based on a renormalization group analysis of the Hertz action with a scalar order parameter. We provide analytic expressions for $T_c$ and $T_{\rm G}$ as a function of the non-thermal control parameter for the quantum phase transition, including logarithmic corrections. The Ginzburg regime between $T_c$ and $T_{\rm G}$ occupies a sizable part of the phase diagram.Comment: 5 pages, 1 figur

Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition

We reexamine the two-dimensional linear O(2) model ($\varphi^4$ theory) in the framework of the nonperturbative renormalization-group. From the flow equations obtained in the derivative expansion to second order and with optimization of the infrared regulator, we find a transition between a high-temperature (disordered) phase and a low-temperature phase displaying a line of fixed points and algebraic order. We obtain a picture in agreement with the standard theory of the Kosterlitz-Thouless (KT) transition and reproduce the universal features of the transition. In particular, we find the anomalous dimension \eta(\Tkt)\simeq 0.24 and the stiffness jump \rho_s(\Tkt^-)\simeq 0.64 at the transition temperature \Tkt, in very good agreement with the exact results \eta(\Tkt)=1/4 and \rho_s(\Tkt^-)=2/\pi, as well as an essential singularity of the correlation length in the high-temperature phase as T\to \Tkt.Comment: v2) Final version as published (with revised title): 10 pages, 10 figure

Self-adjoint symmetry operators connected with the magnetic Heisenberg ring

We consider symmetry operators a from the group ring C[S_N] which act on the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We investigate such symmetry operators a which are self-adjoint (in a sence defined in the paper) and which yield consequently observables of the Heisenberg model. We prove the following results: (i) One can construct a self-adjoint idempotent symmetry operator from every irreducible character of every subgroup of S_N. This leads to a big manifold of observables. In particular every commutation symmetry yields such an idempotent. (ii) The set of all generating idempotents of a minimal right ideal R of C[S_N] contains one and only one idempotent which ist self-adjoint. (iii) Every self-adjoint idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k which are also self-adjoint and pairwise orthogonal. We give a computer algorithm for the calculation of such decompositions. Furthermore we present 3 additional algorithms which are helpful for the calculation of self-adjoint operators by means of discrete Fourier transforms of S_N. In our investigations we use computer calculations by means of our Mathematica packages PERMS and HRing.Comment: 13 page

An alternative approach to the construction of Schur-Weyl transform

We propose an alternative approach for the construction of the unitary matrix which performs generalized unitary rotations of the system consisting of independent identical subsystems (for example spin system). This matrix, when applied to the system, results in a change of degrees of freedom, uncovering the information hidden in non-local degrees of freedom. This information can be used, inter alia, to study the structure of entangled states, their classification and may be useful for construction of quantum algorithms.Comment: 6 page

Turning a First Order Quantum Phase Transition Continuous by Fluctuations: General Flow Equations and Application to d-Wave Pomeranchuk Instability

We derive renormalization group equations which allow us to treat order parameter fluctuations near quantum phase transitions in cases where an expansion in powers of the order parameter is not possible. As a prototypical application, we analyze the nematic transition driven by a d-wave Pomeranchuk instability in a two-dimensional electron system. We find that order parameter fluctuations suppress the first order character of the nematic transition obtained at low temperatures in mean-field theory, so that a continuous transition leading to quantum criticality can emerge