R J Baxter 1982 London: Academic xii + 486 pp price £43.60 Over the past few years there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them. Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944.

Exactly Solved Models in Statistical Mechanics

One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral models on a lattice Theory of scalar products Form factors Mean value of operator Q Assymptotics of correlation functions Temperature correlation functions Appendices References.

Quantum Inverse Scattering Method and Correlation Functions

We study a certain random groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.

Shape Fluctuations and Random Matrices

accademiche [38]. Ada [45]. Adrian [45]. African [56]. Age [39, 49, 61]. Al [23]. Al-Rawi [23]. Aldous [68]. Alex [15]. Allure [46]. America [60, 66]. American [49, 69, 61, 52]. ancienne [25]. Andreas [28]. Angela [42]. Animals [16]. Ann [26]. Anna [19, 47]. Annotated [46]. Annotations [28]. Anti [37]. Anti-Copernican [37]. Antibiotic [64]. Anxiety [51]. Apocalyptic [61]. Archaeology [26]. Ark [36]. Artisan [32]. Asylum [48]. Atri [54]. Audra [65]. Australia [41]. Authorship [15]. Axelle [29].

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A Complete Bibliography of Publications in Isis, 2000{2009

Quantum inverse scattering method and correlation functions

Space and time dependent correlation functions in the Heisenberg XX0 chain (in the transverse magnetic field) are expressed in terms of Fredholm determinants of linear integral operators. This is done in order to evaluate asymptotics of these correlations, which we shall do in next paper.

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Temperature correlation functions in the XX0 Heisenberg chain. I

The problem of the form of the ‘arctic’ curve of the six-vertex model with domain wall boundary conditions in its disordered regime is addressed. It is well-known that in the scaling limit the model exhibits phase-separation, with regions of order and disorder sharply separated by a smooth curve, called the arctic curve. To find this curve, we study a multiple integral representation for the emptiness formation probability, a correlation function devised to detect spatial transition from order to disorder. We conjecture that the arctic curve, for arbitrary choice of the vertex weights, can be characterized by the condition of condensation of almost all roots of the corresponding saddle-point equations at the same, known, value. In explicit calculations we restrict to the disordered regime for which we have been able to compute the scaling limit of certain generating function entering the saddle-point equations. The arctic curve is obtained in parametric form and appears to be a non-algebraic curve in general; it turns into an algebraic one in the so-called root-of-unity cases. The arctic curve is also discussed in application to the limit shape of q-enumerated (with 0<q≤4) large alternating sign matrices. In particular, as q→0 the limit shape tends to a nontrivial limiting curve, given by a relatively simple equation.

The Arctic Curve of the Domain-Wall Six-Vertex Model

We revisit the problem of determining the Arctic curve in the six-vertex model with domain wall boundary conditions. We describe an alternative method, by which we recover the previously conjectured analytic expression in the square domain. We adapt the method to work for a large class of domains, and for other models exhibiting limit shape phenomena. We study in detail some examples, and derive, in particular, the Arctic curve of the six-vertex model in a triangoloid domain at the ice point.

Arctic Curves of the Six-Vertex Model on Generic Domains: The Tangent Method

The Birth of String Theory

http://theory.fi.infn.it/colomo/dirpapers/pla92a.pdf

Filippo Colomo

Papers

Temperature correlation functions in the XX0 Heisenberg chain. I

The Arctic Curve of the Domain-Wall Six-Vertex Model

Arctic Curves of the Six-Vertex Model on Generic Domains: The Tangent Method

The Birth of String Theory

Correlators in the Heisenberg XXO chain as Fredholm determinants