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Models in Statistical Physics and Quantum Field Theory (Paperback, Softcover reprint of the original 1st ed. 1988)
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Models in Statistical Physics and Quantum Field Theory (Paperback, Softcover reprint of the original 1st ed. 1988)
Series: Trieste Notes in Physics
Expected to ship within 18 - 22 working days
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In these lectures we summarize certain results on models in
statistical physics and quantum field theory and especially
emphasize the deep relation ship between these subjects. From a
physical point of view, we study phase transitions of realistic
systems; from a more mathematical point of view, we describe field
theoretical models defined on a euclidean space-time lattice, for
which the lattice constant serves as a cutoff. The connection
between these two approaches is obtained by identifying partition
functions for spin models with discretized functional integrals.
After an introduction to critical phenomena, we present methods
which prove the existence or nonexistence of phase transitions for
the Ising and Heisenberg models in various dimensions. As an
example of a solvable system we discuss the two-dimensional Ising
model. Topological excitations determine sectors of field
theoretical models. In order to illustrate this, we first discuss
soliton solutions of completely integrable classical models.
Afterwards we dis cuss sectors for the external field problem and
for the Schwinger model. Then we put gauge models on a lattice,
give a survey of some rigorous results and discuss the phase
structure of some lattice gauge models. Since great interest has
recently been shown in string models, we give a short introduction
to both the classical mechanics of strings and the bosonic and
fermionic models. The formulation of the continuum limit for
lattice systems leads to a discussion of the renormalization group,
which we apply to various models."
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