Physica A 189 (1992) 611-615 North-Holland The three-dimensional Ising model in a temperature gradient Alex Hansen and Dietrich Stauffer 1 Groupe MatiOre Condens~e et Mat&iaux, URA CNRS 804, Universitd de Rennes 1, F-35042 Rennes Cedex, France Received 2 July 1992 Revised manuscript received 16 July 1992 The critical temperature T c and the correlation length exponent v for the three-dimensional Ising model is determined via the gradient method. By numerical studies of systems of size up to 3603, we determine the correlation length exponent v = 0.62-+ 0.01 in comparison to the best estimates ranging from 0.624 to 0.630. It may seem a slight contradiction to study equilibrium 'thermodynamical quantities by keeping the system in a steady-state non-equilibrium situation. However, such a method has proven very successful, first in connection with percolation [1], and later with spin systems [2,3]. In this note we study the three-dimensional Ising model held in a fixed temperature gradient. With such an arrangement, the Ising magnet will be magnetized on the side which is colder than the critical temperature for spontaneous magnetization, and will be a paramagnet on the other side. In the region where the temperature passes through the critical temperature T c, a domain of strong fluctuations appears. The width of this region is controlled by the temperature gradient- and it is this control that allows us to extract information on the critical point. We use this method to extract the correlation length exponent v and the critical temperature T c using systems of size up to 3603. The determination of v is very accurate, yielding a value v = 0.62 _+ 0.01 in comparison to earlier values in the literature ranging from 0.624 to 0.630 (see ref. [4], where earlier literature is cited). Our system is a cubic lattice of size L × L × L. At each node there is a spin which may take the values ---1. The spins interact via a nearest-neighbor coupling J. In two perpendicular directions we impose helical boundary 1Present and permanent address: Institute for Theoretical Physics, Cologne University, W-5000 Cologne 41, Germany. 0378-4371/92/$05.00 t~ 1992-Elsevier Science Publishers B,V. All rights reserved