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 $\omega_1=e^{\epsilon_1/k_B T}$ between (nonconsecutive) monomers on nearest-neighbor (NN) sites, an additional energy $\epsilon_2$ 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 ($\theta$-) line. This $\theta$-line is found even when one of the interactions is repulsive, existing for $\omega_1$ in the range $[0,\infty)$, i. e., for $\epsilon_1/k_B T$ in the range $[-\infty,\infty)$. Counterintuitively, a $\theta$-point exists even for an infinite repulsion between NN monomers ($\omega_1=0$), 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 $\omega_2=0$, 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 $\beta=5.7$ simulations, which uses an $a \approx 0.18$ 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