We prove the exact relations between the critical exponents and the susceptibility, implied by the Haldane Luttinger liquid conjecture, for a generic lattice fermionic model or a quantum spin chain with short range weak interaction. The validity of such relations was only checked in some special solvable models, but there was up to now no proof of their validity in non-solvable models.

We consider a model of assisted diffusion of hard-core particles on a line. In this model, a particle can jump left or right by two steps to an unoccupied site, but only if the the site in between is occupied. We show that this model is strongly non-ergodic, and the phase space breaks up into mutually disconnected sectors. The number of such sectors increases as the exponential of the size of t...

Space and time dependent correlation functions in the Heisenberg XX0 chain (in transverse magnetic field) are expressed in terms of Fredholm determinants of linear integral operators at all temperatures. The obtained expression allows useful computation of spectral shapes. Moreover, these determinant expressions allow to evaluate the asymptotic behaviour of correlation functions.

Having introduced the magnon in part I and the spinon in part II as the relevant quasi-particles for the interpretation of the spectrum of low-lying excitations in the one-dimensional (1D) s=1/2 Heisenberg ferromagnet and antiferromagnet, respectively, we now study the low-lying excitations of the Heisenberg antiferromagnet in a magnetic field and interpret these collective states as composites...

We present new results and give a concise review of recent previous results on the asymptotics for large spin of the low-lying spectrum of the ferromagnetic XXZ Heisenberg chain with kink boundary conditions. Our main interest is to gain detailed information on the interface ground states of this model and the low-lying excitations above them. The new and most detailed results are obtained usin...

We consider a special correlation function in the isotropic spin-1 2 Heisenberg antiferromagnet. It is the probability of nding a ferromagnetic string of (adjacent) spins in the antiferromagnetic ground state. We give two diierent representations for this correlation function. Both of them are exact at any distance, but one becomes more eeective for the description of long distance behaviour, t...

Critical phenomena of ferromagnetic transition in colossal magnetoresistance manganites are theoretically studied. Concerning the critical exponents for this transition, there still remains controversy among experimental results. In order to clarify intrinsic physics of the manganites through a comparison with theoretical prediction, we investigate the critical phenomena of double-exchange mode...

In its most general formulation a quantum kinematical system is described by a Heisenberg group; the ”configuration space” in this case corresponds to a maximal isotropic subgroup. We study irreducible models for Heisenberg groups based on compact maximal isotropic subgroups. It is shown that if the Heisenberg group is 2-regular, but the subgroup is not, the ”vacuum sector” of the irreducible r...

In agreement with the Harris criterion, asymptotic critical exponents of threedimensional (3d) Heisenberg-like magnets are not influenced by weak quenched dilution of non-magnetic component. However, often in the experimental studies of corresponding systems concentrationand temperature-dependent exponents are found with values differing from those of the 3d Heisenberg model. In our study, we u...

From an 0 (E)-calculation (E = 6 d) of the dynamical spin correlation function in a Heisenberg system for T 2 T, an expression for that function applicable in dimension d= 3 is deduced. It comprises the expected limiting behaviour in different sectors of the critical region. It has been shown that the MaiMazenko model of a Heisenberg ferromagnet [I], evaluated within an &-expansion, E = 6 d [2,...