767,967 research outputs found
O(2) symmetry breaking vs. vortex loop percolation
We study with lattice Monte Carlo simulations the relation of global O(2)
symmetry breaking in three dimensions to the properties of a geometrically
defined vortex loop network. We find that different definitions of constructing
a network lead to different results even in the thermodynamic limit, and that
with typical definitions the percolation transition does not coincide with the
thermodynamic phase transition. These results show that geometrically defined
percolation observables need not display universal properties related to the
critical behaviour of the system, and do not in general survive in the field
theory limit.Comment: 14 pages; references added, version to appear in Phys.Lett.
Progress towards quantum simulating the classical O(2) model
We connect explicitly the classical model in 1+1 dimensions, a model
sharing important features with lattice gauge theory, to physical models
potentially implementable on optical lattices and evolving at physical time.
Using the tensor renormalization group formulation, we take the time continuum
limit and check that finite dimensional projections used in recent proposals
for quantum simulators provide controllable approximations of the original
model. We propose two-species Bose-Hubbard models corresponding to these finite
dimensional projections at strong coupling and discuss their possible
implementations on optical lattices using a Rb and K Bose-Bose
mixture.Comment: 7 pages, 6 figures, uses revtex, new material and one author added,
as to appear in Phys. Rev.
Critical behavior of O(2)xO(N) symmetric models
We investigate the controversial issue of the existence of universality
classes describing critical phenomena in three-dimensional statistical systems
characterized by a matrix order parameter with symmetry O(2)xO(N) and
symmetry-breaking pattern O(2)xO(N) -> O(2)xO(N-2). Physical realizations of
these systems are, for example, frustrated spin models with noncollinear order.
Starting from the field-theoretical Landau-Ginzburg-Wilson Hamiltonian, we
consider the massless critical theory and the minimal-subtraction scheme
without epsilon expansion. The three-dimensional analysis of the corresponding
five-loop expansions shows the existence of a stable fixed point for N=2 and
N=3, confirming recent field-theoretical results based on a six-loop expansion
in the alternative zero-momentum renormalization scheme defined in the massive
disordered phase.
In addition, we report numerical Monte Carlo simulations of a class of
three-dimensional O(2)xO(2)-symmetric lattice models. The results provide
further support to the existence of the O(2)xO(2) universality class predicted
by the field-theoretical analyses.Comment: 45 pages, 20 figs, some additions, Phys.Rev.B in pres
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