Ž . Fluid Phase Equilibria 150–151 1998 583–589 Phase coexistence in confined Ising systems: a density matrix renormalization approach Enrico Carlon a, ) , Andrzej Drzewinski b ´ a Institute for Theoretical Physics, Katholieke UniÕersiteit LeuÕen, LeuÕen B-3001, Belgium b Institute for Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 937, 50-950 Wrocław 2 Poland Abstract Using a density matrix renormalization approach we have calculated the phase diagram of a two-dimensio Ising model confined between two infinite walls, with opposing surface fields and a bulk field which grows linearly as a function of the distance from the walls and models the effect of gravity on a confined fluid. In th absence of gravity, two-phase coexistence is restricted to temperatures below the wetting temperature as po w Ž . x outby Parry and Evans A.O.Parry,R. Evans,Phys.Rev.Lett.64, 1990 439 .We find that the competing effects ofgravity and surface fields restore the ‘ordinary’ finite size scaling to the bulk critical point,in agreement with previous mean-field results. We have calculated the exponents related to the shift toward the critical point in the limit L ™ `, where L is the distance between the walls and we have found good agreement with previous scaling assumptions. Magnetization profiles calculated from a solid-on-solid Hamiltonian agree well with density matrix renormalization results for temperatures not too close to the bulk critical temperatu q 1998 Elsevier Science B.V. All rights reserved. Keywords: Finite size scaling; Liquid–liquid equilibria; Statistical mechanics; Vapor–liquid equilibria; Wetting 1.Introduction Finite size and surface effects may have a strong influence on the thermodynamics of a physical system. A well known example is a fluid confined between two parallel plates where liquid–vapor condensation occurs at a lowerpressure than in thebulk, a phenomenon known as capillary wx condensation 1 . A familiarand simple model thatmimics this effect is the Ising model confined between two w x identical parallel walls separated by a finite distance L 2,3 . Surface fields acting on the spins at the ) Corresponding author. Tel.: q32-16-327248; fax: q32-16-327886; e-mail: enrico@tfdec1.fys.kuleuven.ac.be 0378-3812r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. Ž . PII: S 0 3 7 8 - 3 8 1 2 9 8 0 0 3 0 5 - 7