2,095 research outputs found
Local defect in a magnet with long-range interactions
We investigate a single defect coupling to the square of the order parameter
in a nearly critical magnet with long-range spatial interactions of the form
, focusing on magnetic droplets nucleated at the defect while
the bulk system is in the paramagnetic phase. Because of the long-range
interaction, the droplet develops a power-law tail which is energetically
unfavorable. However, as long as , the tail contribution to the
droplet free energy is subleading in the limit of large droplets; and the free
energy becomes identical to the case of short-range interactions. We also study
the droplet quantum dynamics with and without dissipation; and we discuss the
consequences of our results for defects in itinerant quantum ferromagnets.Comment: 8 pages, 5 eps figures, final version, as publishe
Quantum and classical localisation and the Manhattan lattice
We consider a network model, embedded on the Manhattan lattice, of a quantum
localisation problem belonging to symmetry class C. This arises in the context
of quasiparticle dynamics in disordered spin-singlet superconductors which are
invariant under spin rotations but not under time reversal. A mapping exists
between problems belonging to this symmetry class and certain classical random
walks which are self-avoiding and have attractive interactions; we exploit this
equivalence, using a study of the classical random walks to gain information
about the corresponding quantum problem. In a field-theoretic approach, we show
that the interactions may flow to one of two possible strong coupling regimes
separated by a transition: however, using Monte Carlo simulations we show that
the walks are in fact always compact two-dimensional objects with a
well-defined one-dimensional surface, indicating that the corresponding quantum
system is localised.Comment: 11 pages, 8 figure
Frustration of decoherence in -shaped superconducting Josephson networks
We examine the possibility that pertinent impurities in a condensed matter
system may help in designing quantum devices with enhanced coherent behaviors.
For this purpose, we analyze a field theory model describing Y- shaped
superconducting Josephson networks. We show that a new finite coupling stable
infrared fixed point emerges in its phase diagram; we then explicitly evidence
that, when engineered to operate near by this new fixed point, Y-shaped
networks support two-level quantum systems, for which the entanglement with the
environment is frustrated. We briefly address the potential relevance of this
result for engineering finite-size superconducting devices with enhanced
quantum coherence. Our approach uses boundary conformal field theory since it
naturally allows for a field-theoretical treatment of the phase slips
(instantons), describing the quantum tunneling between degenerate levels.Comment: 11 pages, 5 .eps figures; several changes in the presentation and in
the figures, upgraded reference
Interacting Electrons and Localized Spins: Exact Results from Conformal Field Theory
We give a brief review of the Kondo effect in a one-dimensional interacting
electron system, and present exact results for the impurity thermodynamic
response based on conformal field theory.Comment: 6 pages LaTeX. To appear in the Proceedings of the 1995 Schladming
Winter School on Low-Dimensional Models in Statistical Physics and Quantum
Field Theor
Effect of Random Impurities on Fluctuation-Driven First Order Transitions
We analyse the effect of quenched uncorrelated randomness coupling to the
local energy density of a model consisting of N coupled two-dimensional Ising
models. For N>2 the pure model exhibits a fluctuation-driven first order
transition, characterised by runaway renormalisation group behaviour. We show
that the addition of weak randomness acts to stabilise these flows, in such a
way that the trajectories ultimately flow back towards the pure decoupled Ising
fixed point, with the usual critical exponents alpha=0, nu=1, apart from
logarithmic corrections. We also show by examples that, in higher dimensions,
such transitions may either become continuous or remain first order in the
presence of randomness.Comment: 13 pp., LaTe
Universal Amplitude Combinations for Self-Avoiding Walks, Polygons and Trails
We give exact relations for a number of amplitude combinations that occur in
the study of self-avoiding walks, polygons and lattice trails. In particular,
we elucidate the lattice-dependent factors which occur in those combinations
which are otherwise universal, show how these are modified for oriented
lattices, and give new results for amplitude ratios involving even moments of
the area of polygons. We also survey numerical results for a wide range of
amplitudes on a number of oriented and regular lattices, and provide some new
ones.Comment: 20 pages, NI 92016, OUTP 92-54S, UCSBTH-92-5
Kinetics of ballistic annihilation and branching
We consider a one-dimensional model consisting of an assembly of two-velocity
particles moving freely between collisions. When two particles meet, they
instantaneously annihilate each other and disappear from the system. Moreover
each moving particle can spontaneously generate an offspring having the same
velocity as its mother with probability 1-q. This model is solved analytically
in mean-field approximation and studied by numerical simulations. It is found
that for q=1/2 the system exhibits a dynamical phase transition. For q<1/2, the
slow dynamics of the system is governed by the coarsening of clusters of
particles having the same velocities, while for q>1/2 the system relaxes
rapidly towards its stationary state characterized by a distribution of small
cluster sizes.Comment: 10 pages, 11 figures, uses multicol, epic, eepic and eepicemu. Also
avaiable at http://mykonos.unige.ch/~rey/pubt.htm
Universal amplitudes in the FSS of three-dimensional spin models
In a MC study using a cluster update algorithm we investigate the finite-size
scaling (FSS) of the correlation lengths of several representatives of the
class of three-dimensional classical O(n) symmetric spin models on a column
geometry. For all considered models we find strong evidence for a linear
relation between FSS amplitudes and scaling dimensions when applying
antiperiodic instead of periodic boundary conditions across the torus. The
considered type of scaling relation can be proven analytically for systems on
two-dimensional strips with periodic bc using conformal field theoryComment: 4 pages, RevTex, uses amsfonts.sty, 3 Figure
Critical behaviour near multiple junctions and dirty surfaces in the two-dimensional Ising model
We consider m two-dimensional semi-infinite planes of Ising spins joined
together through surface spins and study the critical behaviour near to the
junction. The m=0 limit of the model - according to the replica trick -
corresponds to the semi-infinite Ising model in the presence of a random
surface field (RSFI). Using conformal mapping, second-order perturbation
expansion around the weakly- and strongly-coupled planes limits and
differential renormalization group, we show that the surface critical behaviour
of the RSFI model is described by Ising critical exponents with logarithmic
corrections to scaling, while at multiple junctions (m>2) the transition is
first order. There is a spontaneous junction magnetization at the bulk critical
point.Comment: Old paper, for archiving. 6 pages, 1 figure, IOP macro, eps
Logarithmic observables in critical percolation
Although it has long been known that the proper quantum field theory
description of critical percolation involves a logarithmic conformal field
theory (LCFT), no direct consequence of this has been observed so far.
Representing critical bond percolation as the Q = 1 limit of the Q-state Potts
model, and analyzing the underlying S_Q symmetry of the Potts spins, we
identify a class of simple observables whose two-point functions scale
logarithmically for Q = 1. The logarithm originates from the mixing of the
energy operator with a logarithmic partner that we identify as the field that
creates two propagating clusters. In d=2 dimensions this agrees with general
LCFT results, and in particular the universal prefactor of the logarithm can be
computed exactly. We confirm its numerical value by extensive Monte-Carlo
simulations.Comment: 11 pages, 2 figures. V2: as publishe
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