The Specific Heat of a Ferromagnetic Film.

Abstract

We analyze the specific heat for the $O(N)$ vector model on a $d$-dimensional film geometry of thickness $L$ using ``environmentally friendly'' renormalization. We consider periodic, Dirichlet and antiperiodic boundary conditions, deriving expressions for the specific heat and an effective specific heat exponent, $α\ef$. In the case of $d=3$, for $N=1$, by matching to the exact exponent of the two dimensional Ising model we capture the crossover for $ξ_L\ra\infty$ between power law behaviour in the limit ${L\overξ_L}\ra\infty$ and logarithmic behaviour in the limit ${L\overξ_L}\ra0$ for fixed $L$, where ${\xi }_L$ is the correlation length in the transverse dimensions.

21 pages of Plain TeX. Postscript figures available upon request from [email protected]

References in corpus (1)

• Effective Critical Exponents for Dimensional Ccrossover and Quantum Systems from an Environmentally Friendly Renormalization Group

Cited by in corpus (3)

• Fluctuation - induced forces in critical fluids
• Dimensional Crossover in the Large N Limit
• Dimensional Reduction, Hard Thermal Loops and the Renormalization Group