90,588 research outputs found
Polymers with nearest- and next nearest-neighbor interactions on the Husimi lattice
The exact grand-canonical solution of a generalized interacting self-avoid
walk (ISAW) model, placed on a Husimi lattice built with squares, is presented.
In this model, beyond the traditional interaction between (nonconsecutive) monomers on nearest-neighbor (NN) sites, an
additional energy is associated to next-NN (NNN) monomers. Three
definitions of NNN sites/interactions are considered, where each monomer can
have, effectively, at most 2, 4 or 6 NNN monomers on the Husimi lattice. The
phase diagrams found in all cases have (qualitatively) the same thermodynamic
properties: a non-polymerized (NP) and a polymerized (P) phase separated by a
critical and a coexistence surface that meet at a tricritical (-) line.
This -line is found even when one of the interactions is repulsive,
existing for in the range , i. e., for in the range . Counterintuitively, a -point exists
even for an infinite repulsion between NN monomers (), being
associated to a coil-"soft globule" transition. In the limit of an infinite
repulsive force between NNN monomers, however, the coil-globule transition
disappears and only a NP-P continuous transition is observed. This particular
case, with , is also solved exactly on the square lattice, using a
transfer matrix calculation, where a discontinuous NP-P transition is found.
For attractive and repulsive forces between NN and NNN monomers, respectively,
the model becomes quite similar to the semiflexible-ISAW one, whose crystalline
phase is not observed here, as a consequence of the frustration due to
competing NN and NNN forces. The mapping of the phase diagrams in canonical
ones is discussed and compared with recent results from Monte Carlo
simulations.Comment: 21 pages, 6 figure
Exact Solution of a Linear Wave Equation in Cosmological General Relativity
A linear second order wave equation is presented based on cosmological
general relativity, which is a space-velocity theory of the expanding Universe.
The wave equation is shown to be exactly solvable, based on the Gaussian
hypergeometric function.Comment: 6 page
The lattice Landau gauge gluon propagator: lattice spacing and volume dependence
The interplay between the finite volume and finite lattice spacing is
investigated using lattice QCD simulations to compute the Landau gauge gluon
propagator. Comparing several ensembles with different lattice spacings and
physical volumes, we conclude that the dominant effects, in the infrared
region, are associated with the use of a finite lattice spacing. The
simulations show that decreasing the lattice spacing, while keeping the same
physical volume, leads to an enhancement of the infrared gluon propagator. In
this sense, the data from simulations, which uses an fm, provides a lower bound for the infinite volume propagator.Comment: Final version to appear in Phys Rev
Transfer-matrix study of a hard-square lattice gas with two kinds of particles and density anomaly
Using transfer matrix and finite-size scaling methods, we study the
thermodynamic behavior of a lattice gas with two kinds of particles on the
square lattice. Only excluded volume interactions are considered, so that the
model is athermal. Large particles exclude the site they occupy and its four
first neighbors, while small particles exclude only their site. Two
thermodynamic phases are found: a disordered phase where large particles occupy
both sublattices with the same probability and an ordered phase where one of
the two sublattices is preferentially occupied by them. The transition between
these phases is continuous at small concentrations of the small particles and
discontinuous at larger concentrations, both transitions are separated by a
tricritical point. Estimates of the central charge suggest that the critical
line is in the Ising universality class, while the tricritical point has
tricritical Ising (Blume-Emery-Griffiths) exponents. The isobaric curves of the
total density as functions of the fugacity of small or large particles display
a minimum in the disordered phase.Comment: 9 pages, 7 figures and 4 table
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