2,448 research outputs found
Shift in critical temperature for random spatial permutations with cycle weights
We examine a phase transition in a model of random spatial permutations which
originates in a study of the interacting Bose gas. Permutations are weighted
according to point positions; the low-temperature onset of the appearance of
arbitrarily long cycles is connected to the phase transition of Bose-Einstein
condensates. In our simplified model, point positions are held fixed on the
fully occupied cubic lattice and interactions are expressed as Ewens-type
weights on cycle lengths of permutations. The critical temperature of the
transition to long cycles depends on an interaction-strength parameter
. For weak interactions, the shift in critical temperature is expected
to be linear in with constant of linearity . Using Markov chain
Monte Carlo methods and finite-size scaling, we find .
This finding matches a similar analytical result of Ueltschi and Betz. We also
examine the mean longest cycle length as a fraction of the number of sites in
long cycles, recovering an earlier result of Shepp and Lloyd for non-spatial
permutations.Comment: v2 incorporated reviewer comments. v3 removed two extraneous figures
which appeared at the end of the PDF
Semi-classical scalar products in the generalised SU(2) model
In these notes we review the field-theoretical approach to the computation of
the scalar product of multi-magnon states in the Sutherland limit where the
magnon rapidities condense into one or several macroscopic arrays. We formulate
a systematic procedure for computing the 1/M expansion of the
on-shell/off-shell scalar product of M-magnon states in the generalised
integrable model with SU(2)-invariant rational R-matrix. The coefficients of
the expansion are obtained as multiple contour integrals in the rapidity plane.Comment: 13 pages, 3 figures. Based on a talk delivered at the X.
International Workshop "Lie Theory and Its Applications in Physics", (LT-10),
Varna, Bulgaria, 17-23 June 201
On the symmetry of good nonlinear codes
It is shown that there are arbitrarily long "good" (in the sense of Gilbert) binary block codes that are preserved under very large permutation groups. This result contrasts sharply with the properties of linear codes: it is conjectured that long cyclic codes are bad, and known that long affine-invariant codes are bad
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