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

Form factors of the xxz heisenberg spin-1/2 finite chain

Quantum inverse scattering method and correlation functions

Quantum phase transitions of the transverse Ising and antiferromagnetic $XXZ$ spin $S=1/2$ chains are studied using quantum discord. Quantum discord allows the measure of quantum correlations present in many-body quantum systems. It is shown that the amount of quantum correlations increases close to the critical points. The observations are in agreement with the information provided by the concurrence, which measures the entanglement of the many-body system.

Quantum discord and quantum phase transition in spin chains

Correlation functions of the XXZ Heisenberg spin- chain in a magnetic field

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

Correlation function of the spin 1/2 XXX antiferromagnet

We consider zero temperature correlation functions of the spin-1/2 XXZ Heisenberg chain in the critical regime −1<Δ≦1 in a magnetic field. Starting from the algebraic Bethe Ansatz we derive representations for various correlation functions in term of determinats of Fredholm integral operators.

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Determinant representation for correlation functions of spin-$1/2$ $XXX$ and $XXZ$ Heisenberg magnets

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

Correlators in the Heisenberg XXO chain as Fredholm determinants

The spectral shape of one-dimensional systems (describing for instance the behaviour of Frenkel excitons) is approached through the exactly solvable model of the XXO Heisenberg quantum spin chain in a transverse magnetic field. Some results for finite size chains concerning 2N-point correlators are presented in detail. In particular, the finite lattice, finite temperature 2-point correlators are explicitly worked out. Moreover, results in closed form are given for 2N-point correlators in the most general situation (finite lattice and thermodynamic limit, finite temperature, finite space and/or time separations). Their relations with frequency moments of the spectral shape are pointed out and the connection with moment expansion through continued fraction representation is given.

/pdf/correlation-functions-in-the-xxo-heisenberg-chain-and-their-o96lnn6l0z.pdf

A. G. Izergin

Papers

Temperature correlation functions in the XX0 Heisenberg chain. I

Correlation function of the spin 1/2 XXX antiferromagnet

Determinant representation for correlation functions of spin-$1/2$ $XXX$ and $XXZ$ Heisenberg magnets

Correlators in the Heisenberg XXO chain as Fredholm determinants

Correlation functions in the XXO Heisenberg chain and their relations with spectral shapes