The aim of this book is to familiarise the reader with the rich collection of ideas, methods and results available in the theory of critical phenomena in systems with confined geometry. The existence of universal features of the finite-size effects arising due to highly correlated classical or quantum fluctuations is explained by the finite-size scaling theory. This theory (1) offers an interpretation of experimental results on finite-size effects in real systems; (2) gives the most reliable tool for extrapolation to the thermodynamic limit of data obtained by computer simulations; (3) revealsThe aim of this book is to familiarise the reader with the rich collection of ideas, methods and results available in the theory of critical phenomena in systems with confined geometry. The existence of universal features of the finite-size effects arising due to highly correlated classical or quantum fluctuations is explained by the finite-size scaling theory. This theory (1) offers an interpretation of experimental results on finite-size effects in real systems; (2) gives the most reliable tool for extrapolation to the thermodynamic limit of data obtained by computer simulations; (3) reveals

Singapore perspectivesJan 1, 2000137 citations

Finite-Size Scaling Theory

V. Rittenberg

Springer eBooksJan 1, 19831 citation

Field theory in a finite geometry: Finite size scaling

Jean Zinn‐Justin

Abstract Computer simulations of critical statistical systems or quantum field theory models are performed with systems where sizes are finite. In transfer matrix calculations, all sizes but one are also finite. In systems where the correlation length is large, it is thus important to understand how the infinite size limit is reached. This problem is investigated in Chapter 19. RG equations allow proving the properties of universality and of finite size scaling. When the correlation length is larger than the linear system size, a phenomenon of dimensional reduction is observed. With periodic boundary conditions, fields have a zero mode. A local expansion generates an effective field theory for the zero mode.Abstract Computer simulations of critical statistical systems or quantum field theory models are performed with systems where sizes are finite. In transfer matrix calculations, all sizes but one are also finite. In systems where the correlation length is large, it is thus important to understand how the infinite size limit is reached. This problem is investigated in Chapter 19. RG equations allow proving the properties of universality and of finite size scaling. When the correlation length is larger than the linear system size, a phenomenon of dimensional reduction is observed. With periodic boundary conditions, fields have a zero mode. A local expansion generates an effective field theory for the zero mode.

Jun 19, 20190 citations

FINITE-SIZE SCALING THEORY

Vladimir Privman A

WORLD SCIENTIFIC eBooksJan 1, 199076 citations

Violation of finite-size scaling for the free energy near criticality

X. S. Chen, V. Dohm

The singular part of the finite-size free energy density $f_s$ of the O( $n$ ) symmetric $ϕ^4$ field theory is calculated for confined geometries of linear size L with periodic boundary conditions in the large-N limit and with Dirichlet boundary conditions in one-loop order. We find that both a sharp cutoff and a subleading long-range interaction cause a non-universal L dependence of $f_s$ near $T_c$ . For film geometry this implies a non-universal critical Casimir force with an algebraic L dependence that dominates the exponential finite-size scaling behavior above $T_c$ for both periodic and Dirichlet boundary conditions.The singular part of the finite-size free energy density $f_s$ of the O($n$) symmetric $ϕ^4$ field theory is calculated for confined geometries of linear size L with periodic boundary conditions in the large-N limit and with Dirichlet boundary conditions in one-loop order. We find that both a sharp cutoff and a subleading long-range interaction cause a non-universal L dependence of $f_s$ near $T_c$. For film geometry this implies a non-universal critical Casimir force with an algebraic L dependence that dominates the exponential finite-size scaling behavior above $T_c$ for both periodic and Dirichlet boundary conditions.

arXiv:cond-mat/0112310Dec 17, 20011 citation

The singular part of the finite-size free energy density

f_s

of the O(

n

) symmetric

ϕ^4

field theory is calculated for confined geometries of linear size L with periodic boundary conditions in the large-N limit and with Dirichlet boundary conditions in one-loop order. We find that both a sharp cutoff and a subleading long-range interaction cause a non-universal L dependence of

f_s

near

T_c

. For film geometry this implies a non-universal critical Casimir force with an algebraic L dependence that dominates the exponential finite-size scaling behavior above

T_c

for both periodic and Dirichlet boundary conditions.