Sine-Gordon Statistical Mechanics

Abstract

The Classical partition-function

$$ Z = \int {D\Pi {\text{ }}D\phi {\text{ }}\exp - } \beta H\left[ \phi \right]$$

(1)

in which ${\beta ^{{ - 1}}} = {k_{B}}T{\text{ and }}H\left[ \phi \right]$ is the sine-Gordon (s-G) Hamiltonian

$$ H\left[ \phi \right] = {\Upsilon _{0}}^{{ - 1}}\int {\left[ {\frac{1}{2}{\Upsilon _{0}}^{2}{\Pi ^{2}} + \frac{1}{2}{\phi _{z}}^{2} + {m^{2}}\left( {1 - \cos \phi } \right)} \right]} dz $$

(2)

has been evaluated by transfer integral methods [1,2].