Dimensional crossover in the non-linear sigma model

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

Abstract


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.

Keywords


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

Full Text:

PDF

Refbacks

  • There are currently no refbacks.


Revista Mexicana de Física

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

Bimonthly publication of Sociedad Mexicana de Física, A.C.
Departamento de Física, 2o. Piso, Facultad de Ciencias, UNAM.
Circuito Exterior s/n, Ciudad Universitaria. C. P. 04510 Ciudad de México.
Apartado Postal 70-348, Coyoacán, 04511 Ciudad de México.
Tel/Fax: (52) 55-5622-4946, (52) 55-5622-4840. rmf@ciencias.unam.mx