649 research outputs found
Entropy-driven phase transition in a polydisperse hard-rods lattice system
We study a system of rods on the 2d square lattice, with hard-core exclusion.
Each rod has a length between 2 and N. We show that, when N is sufficiently
large, and for suitable fugacity, there are several distinct Gibbs states, with
orientational long-range order. This is in sharp contrast with the case N=2
(the monomer-dimer model), for which Heilmann and Lieb proved absence of phase
transition at any fugacity. This is the first example of a pure hard-core
system with phases displaying orientational order, but not translational order;
this is a fundamental characteristic feature of liquid crystals
Failure of Mean Field Theory at Large N
We study strongly coupled lattice QCD with colors of staggered fermions
in 3+1 dimensions. While mean field theory describes the low temperature
behavior of this theory at large , it fails in the scaling region close to
the finite temperature second order chiral phase transition. The universal
critical region close to the phase transition belongs to the 3d XY universality
class even when becomes large. This is in contrast to Gross-Neveu models
where the critical region shrinks as (the number of flavors) increases and
mean field theory is expected to describe the phase transition exactly in the
limit of infinite . Our work demonstrates that close to second order phase
transitions infrared fluctuations can sometimes be important even when is
strictly infinite.Comment: 4 pages, 3 figure
A Class of Parameter Dependent Commuting Matrices
We present a novel class of real symmetric matrices in arbitrary dimension
, linearly dependent on a parameter . The matrix elements satisfy a set
of nontrivial constraints that arise from asking for commutation of pairs of
such matrices for all , and an intuitive sufficiency condition for the
solvability of certain linear equations that arise therefrom. This class of
matrices generically violate the Wigner von Neumann non crossing rule, and is
argued to be intimately connected with finite dimensional Hamiltonians of
quantum integrable systems.Comment: Latex, Added References, Typos correcte
Spectral microscopic mechanisms and quantum phase transitions in a 1D correlated problem
In this paper we study the dominant microscopic processes that generate
nearly the whole one-electron removal and addition spectral weight of the
one-dimensional Hubbard model for all values of the on-site repulsion . We
find that for the doped Mott-Hubbard insulator there is a competition between
the microscopic processes that generate the one-electron upper-Hubbard band
spectral-weight distributions of the Mott-Hubbard insulating phase and
finite-doping-concentration metallic phase, respectively. The spectral-weight
distributions generated by the non-perturbative processes studied here are
shown elsewhere to agree quantitatively for the whole momentum and energy
bandwidth with the peak dispersions observed by angle-resolved photoelectron
spectroscopy in quasi-one-dimensional compounds.Comment: 18 pages, 2 figure
A note on density correlations in the half-filled Hubbard model
We consider density-density correlations in the one-dimensional Hubbard model
at half filling. On intuitive grounds one might expect them to exhibit an
exponential decay. However, as has been noted recently, this is not obvious
from the Bethe Ansatz/conformal field theory (BA/CFT) approach. We show that by
supplementing the BA/CFT analysis with simple symmetry arguments one can easily
prove that correlations of the lattice density operators decay exponentially.Comment: 3 pages, RevTe
Irreducibility criterion for a finite-dimensional highest weight representation of the sl(2) loop algebra and the dimensions of reducible representations
We present a necessary and sufficient condition for a finite-dimensional
highest weight representation of the loop algebra to be irreducible. In
particular, for a highest weight representation with degenerate parameters of
the highest weight, we can explicitly determine whether it is irreducible or
not. We also present an algorithm for constructing finite-dimensional highest
weight representations with a given highest weight. We give a conjecture that
all the highest weight representations with the same highest weight can be
constructed by the algorithm. For some examples we show the conjecture
explicitly. The result should be useful in analyzing the spectra of integrable
lattice models related to roots of unity representations of quantum groups, in
particular, the spectral degeneracy of the XXZ spin chain at roots of unity
associated with the loop algebra.Comment: 32 pages with no figure; with corrections on the published versio
The repulsive lattice gas, the independent-set polynomial, and the Lov\'asz local lemma
We elucidate the close connection between the repulsive lattice gas in
equilibrium statistical mechanics and the Lovasz local lemma in probabilistic
combinatorics. We show that the conclusion of the Lovasz local lemma holds for
dependency graph G and probabilities {p_x} if and only if the independent-set
polynomial for G is nonvanishing in the polydisc of radii {p_x}. Furthermore,
we show that the usual proof of the Lovasz local lemma -- which provides a
sufficient condition for this to occur -- corresponds to a simple inductive
argument for the nonvanishing of the independent-set polynomial in a polydisc,
which was discovered implicitly by Shearer and explicitly by Dobrushin. We also
present some refinements and extensions of both arguments, including a
generalization of the Lovasz local lemma that allows for "soft" dependencies.
In addition, we prove some general properties of the partition function of a
repulsive lattice gas, most of which are consequences of the alternating-sign
property for the Mayer coefficients. We conclude with a brief discussion of the
repulsive lattice gas on countably infinite graphs.Comment: LaTex2e, 97 pages. Version 2 makes slight changes to improve clarity.
To be published in J. Stat. Phy
Algebraic Bethe ansatz approach for the one-dimensional Hubbard model
We formulate in terms of the quantum inverse scattering method the algebraic
Bethe ansatz solution of the one-dimensional Hubbard model. The method
developed is based on a new set of commutation relations which encodes a hidden
symmetry of 6-vertex type.Comment: appendix additioned with Boltzmann weigths and R-matrix. Version to
be published in J.Phys.A:math.Gen. (1997
Strong-coupling expansions for the anharmonic Holstein model and for the Holstein-Hubbard model
A strong-coupling expansion is applied to the anharmonic Holstein model and
to the Holstein-Hubbard model through fourth order in the hopping matrix
element. Mean-field theory is then employed to determine transition
temperatures of the effective (pseudospin) Hamiltonian. We find that anharmonic
effects are not easily mimicked by an on-site Coulomb repulsion, and that
anharmonicity strongly favors superconductivity relative to charge-density-wave
order. Surprisingly, the phase diagram is strongly modified by relatively small
values of the anharmonicity.Comment: 34 pages, typeset in ReVTeX, 11 encapsulated postscript files
include
The Grand-Canonical Asymmetric Exclusion Process and the One-Transit Walk
The one-dimensional Asymmetric Exclusion Process (ASEP) is a paradigm for
nonequilibrium dynamics, in particular driven diffusive processes. It is
usually considered in a canonical ensemble in which the number of sites is
fixed. We observe that the grand-canonical partition function for the ASEP is
remarkably simple. It allows a simple direct derivation of the asymptotics of
the canonical normalization in various phases and of the correspondence with
One-Transit Walks recently observed by Brak et.al.Comment: Published versio
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