Dimensional crossover in the non-linear sigma model

Denjoe O' Connor. , C. R, J. A


We consider dimensional crossover for an $O(N)$ model on a $d$-dimensional layered geometry of thickness $L$, in the $\sigma$-model limit, using ``environmentally friendly'' renormalization. We show how to derive critical temperature shifts, giving explicit results to one loop. We also obtain expressions for the effective critical exponents $\delta_{\rm eff}$ and $\beta_{\rm eff}$ that interpolate between their characteristic fixed point values associated with a $d$ and $(d-1)$-dimensional system in the limits $T\rightarrow T_c(L)$, with $L(T-T_c(L))^{\nu}\rightarrow\infty$, and $T\rightarrow T_c(L)$ for $L$ fixed respectively, where $T_c(L)$ is the $L$-dependent critical temperature of the system.


Renormalization group; dimensional crossover; critical phenomena; non-linear -model

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Revista Mexicana de Física

ISSN: 2683-2224 (on line), 0035-001X (print)

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