Heisenberg Field Theory

The Heisenberg Group and Conformal Field Theory

A mathematical construction of the conformal field theory (CFT) associated to a compact torus, also called the “nonlinear σ-model” or “lattice-CFT”, is given. Underlying this approach to CFT is a unitary modular functor, the construction of which follows from a “Quantization commutes with reduction”type of theorem for unitary quantizations of the moduli spaces of holomorphic torusbundles and ac...

Quantum Field Theory in the Heisenberg Picture

Mean field theory for Heisenberg spin glasses

2014 The infinite-ranged spin glass model is studied in the general case of m-component spins. Results for the magnetization laws, the shape of the phase diagram, the nature of the transitions are presented. J. Physique LETTRES 42 (1981) L-103 L-106 1 PI MARS 1981, Classification Physics Abstracts 05.50 75.50K The infinite-ranged model [1], introduced by D. Sherrington and S. Kirkpatrick (SK), ...

Mean field theory of a quantum heisenberg spin glass

A full mean-field solution of a quantum Heisenberg spin-glass model is presented in a large- N limit. A spin-glass transition is found for all values of the spin S. The quantum critical regime associated with the quantum transition at S = 0 and the various regimes in the spin-glass phase at high spin are analyzed. The specific heat is shown to vanish linearly with temperature. In the spin-glass...

Non - linear Field Theory of a Frustrated Heisenberg Spin Chain

We derive a continuum field theory for the Majumdar-Ghosh model in the large-S limit, where the field takes values in the manifold of the SO(3) group. No topological term is induced in the action and the cases for integer spin and half-integer spin appear to be indistinguishable. A one-loop β−function calculation indicates that the theory flows towards a strong coupling (disordered) phase at lo...