0 N ov 1 99 9 Intersecting Loop Models on Z d : Rigorous Results

0 O ct 1 99 9 Intersecting Loop Models on Z d : Rigorous Results

We consider a general class of (intersecting) loop models in d dimensions, including those related to high-temperature expansions of well-known spin models. We find that the loop models exhibit some interesting features – often in the “unphysical” region of parameter space where all connection with the original spin Hamiltonian is apparently lost. For a particular n = 2, d = 2 model, we establi...

Intersecting loop models on Z: rigorous results

Ž . We consider a general class of intersecting loop models in d dimensions, including those related to high-temperature expansions of well-known spin models. We find that the loop models exhibit some interesting features – often in the ‘‘unphysical’’ region of parameter space where all connection with the original spin Hamiltonian is apparently lost. For a particular ns2, ds2 model, we establi...

N ov 1 99 9 RIGOROUS PROBABILISTIC ANALYSIS OF EQUILIBRIUM CRYSTAL SHAPES

The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results which have been obtained, both in two and higher dimensions. In particular, we describe how the phenomenological Wulff and Winterbottom constructions can be derived from the microscopic description provided by the equilibrium statistical mechanics of l...

0 N ov 1 99 9 Exact ground state for 1 D electronic models

We have found the exact ground state for two electronic models on a linear chain. The first model describes half-filling electron system in the ferromagnet– antiferromagnet transition point. In the singlet ground state the spin correlators show giant spiral magnetic ordering with the period of a spiral equals to the system size. The second electronic model describes the point where the ground s...

/ 97 11 02 3 v 1 2 7 N ov 1 99 7 Evidence of φ → π 0 π 0 γ and φ → π 0