Third-order phase transition in random tilings

We consider the domino tilings of an Aztec diamond with a cut-off corner of macroscopic square shape and given size, and address the bulk properties of tilings as the size is varied. We observe that the free energy exhibits a third-order phase transition when the cut-off square, increasing in size, reaches the arctic ellipse---the phase separation curve of the original (unmodified) Aztec diamond. We obtain this result by studying the thermodynamic limit of certain nonlocal correlation function of the underlying six-vertex model with domain wall boundary conditions, the so-called emptiness formation probability (EFP). We consider EFP in two different representations: as a tau-function for Toda chains and as a random matrix model integral. The latter has a discrete measure and a linear potential with hard walls; the observed phase transition shares properties with both Gross-Witten-Wadia and Douglas-Kazakov phase transitions.Comment: 21 pages, 6 figures; v3: journal version with misprints in text and Fig. 3 corrected; footnote added at page

Emptiness formation probability of the six-vertex model and the sixth Painlev\'e equation

We show that the emptiness formation probability of the six-vertex model with domain wall boundary conditions at its free-fermion point is a $\tau$-function of the sixth Painlev\'e equation. Using this fact we derive asymptotics of the emptiness formation probability in the thermodynamic limit.Comment: 48 pages, 3 figures; v2: appendix A and comments at the end of Sect. 4.2 adde

Emptiness formation probability in the domain-wall six-vertex model

The emptiness formation probability in the six-vertex model with domain wall boundary conditions is considered. This correlation function allows one to address the problem of limit shapes in the model. We apply the quantum inverse scattering method to calculate the emptiness formation probability for the inhomogeneous model. For the homogeneous model, the result is given both in terms of certain determinant and as a multiple integral representation.Comment: 22 pages, no figure

Baxter Q-operators for integrable DST chain

Following the procedure, described in the paper nlin.SI/0003002, for the integrable DST chain we construct Baxter Q-operators as the traces of monodromy of some M-operators, that act in quantum and auxiliary spaces. Within this procedure we obtain two basic M-operators and derive some functional relations between them such as intertwining relations and wronskian-type relations between two basic Q-operators.Comment: LaTeX, 12 pages, minor changes in the text, references adde

On the Algebraic Bethe Ansatz for XXX spin chain: creation operators "beyond the equator"

Considering the XXX spin-1/2 chain in the framework of the Algebraic Bethe Ansatz (ABA) we make the following short comment: the product of the creation operators corresponding to the recently found solution of the Bethe equations "on the wrong side of the equator" (hep-th/9808153) is just zero (not only its action on the pseudovacuum).Comment: LaTeX, 4 page

Baxters's Q-operators for the simplest q-deformed model

In the present paper we describe the procedure of the Q-operators construction for the q-deformed model, described by the Lax operator, which is important to formulate the Bethe ansatz for the Sin-Gordon model. This Lax operator can also be considered as some massless limit of the Lax operator of SG model. We constructed two R-operators which are the universal intertwiners for the Lax operators. The traces of its monodromies over the auxiliary space are Baxter operators i.e. the operator solutions of T-Q equation. We also found the intertwining relations which imply the mutual commutativity of the corresponding Q-operators.Comment: 11 page

Temperature correlators in the one-dimensional Hubbard model in the strong coupling limit

We consider the one-dimensional Hubbard model with the infinitely strong repulsion. The two-point dynamical temperature correlation functions are calculated. They are represented as Fredholm determinants of linear integrable integral operators.Comment: 14 pages, LaTeX; some comments are added, a few misprints are correcte

Scaling of many-particle correlations in a dissipative sandpile

The two dimensional directed sandpile with dissipation is transformed into a (1+1) dimensional problem with discrete space and continuous `time'. The master equation for the conditional probability that K grains preserve their initial order during an avalanche can thereby be solved exactly, and an explicit expression is given for the asymptotic form of the solution for an infinite as well as for a semi-infinite lattice in the horizontal direction. Non-trivial scaling is found in both cases. This conditional probability of the sandpile model is shown to be equal to a K-spin correlation function of the Heisenberg XX spin chain, and the sandpile problem is also shown to be equivalent to the `random-turns' version of vicious walkers.Comment: 17 pages, no figure

The Extended Chiral Bosonisation And Pion-Diquark Effective Action

We consider bosonisation of the low-energy QCD based on integrating the anomaly of the extended chiral (E$\chi$) transformation which depends both on pseudoscalar meson and scalar diquark fields as parameters. The relationship between extended chiral and usual chiral anomalies and related anomalous actions is studied. The effective action for the extended chiral field \U depending on complete set of anomalous generators of the E$\chi$-transformation is given. The terms of this effective action relevant to interaction of pions and $\bar 3_c$ scalar diquarks are written down explicitly.Comment: LaTeX, 10 pages, no figures, some minor misprints correcte

Possible nature of Z+(4430)Z^+(4430)

We discuss exotic states X(3872) and $Z^+(4430)$, observed recently in experiment Belle. The QCD-string based explanation is suggested.Comment: 5 pages, 6 figure