PHYSICS REPORTS (Review Section of Physics Letters) 103, Nos. 1-4 (1984) 47-58. North-Holland, Amsterdam Strip-these for Random Systems J. VANNIMENUS and J.P. NADAL Groupe de Physique des Solides de l'Ecole Normale Sup(rieure, 24 rue Lhomond, 75231 Paris Cedex 05, France Abstract: A useful approach to critical phenomena consists in studying systems infinite in one dimension ("strips" or bars) via transfer-matrix methods and finite size scaling. Its application to random systems is reviewed, with emphasis on directed models and on resistor networks as typical examples of the numerical methods used in practice. I. Introduction The "strip-these" is a nickname [1] for an approach to critical phenomena that consists in studying systems infinite in one direction (rather than cubes for instance). That approach first advocated by Nightingale [2] has been used for a wide variety of problems in the last three years and has proved quite efficient, mostly in two dimensions. Nightingale [3] has given recently an account of the method and of its applications to pure thermodynamic systems. Here we present a short review of the work on random systems that originated with a study of percolation [4], stressing the different ways to implement the method in practice. The general strategy is based on the use of transfer matrices to obtain the properties of strips (or bars in three dimensions) of different widths. The results are then analyzed using the scaling equations for a system of finite size near a critical point. This programme can rarely be carried out analytically, and one has to rely on numerical methods. In favorable cases like percolation exact results (in a numerical sense) can be obtained on strips large enough to give precise estimates of critical exponents. In other situations, the properties of the strips have to be obtained by some type of Monte Carlo simulations: the results are less accurate, but still compare favorably with other approaches. Two examples are discussed in more detail below to illustrate both cases: directed systems (percolation and lattice animals), and conduction in random resistor networks. 2. General method Far from a critical point, the results obtained on finite systems can in general be extrapolated directly to obtain the properties of the bulk system. Near a critical point, however, a more sophisticated analysis becomes necessary because the size effects are quite non-trivial. The theory of finite-size scaling indicates how this analysis has to be carried out, thus giving the possibility to take advantage of these effects. We take here a practical point of view and do not discuss the validity of this theory- see ref. [5] for such discussions.