Skip to main content

Designer spin systems via inverse statistical mechanics

Author(s): DiStasio, Robert A.; Marcotte, Étienne; Car, Roberto; Stillinger, Frank H.; Torquato, Salvatore

To refer to this page use: http://arks.princeton.edu/ark:/88435/pr1151c
 Abstract: In this work, we extend recent inverse statistical-mechanical methods developed for many-particle systems to the case of spin systems. For simplicity, we focus in this initial study on the two-state Ising model with radial spin-spin interactions of finite range (i.e., extending beyond nearest-neighbor sites) on the square lattice under periodic boundary conditions. Our interest herein is to find the optimal set of shortest-range pair interactions within this family of Hamiltonians, whose corresponding ground state is a targeted spin configuration such that the difference in energies between the energetically closest competitor and the target is maximized. For an exhaustive list of competitors, this optimization problem is solved exactly using linear programming. The possible outcomes for a given target configuration can be organized into the following three solution classes: unique (nondegenerate) ground state (class I), degenerate ground states (class II), and solutions not contained in the previous two classes (class III). We have chosen to study a general family of striped-phase spin configurations comprised of alternating parallel bands of up and down spins of varying thicknesses and a general family of rectangular block checkerboard spin configurations with variable block size, which is a generalization of the classic antiferromagnetic Ising model. Our findings demonstrate that the structurally anisotropic striped phases, in which the thicknesses of up- and down-spin bands are equal, are unique ground states for isotropic short-ranged interactions. By contrast, virtually all of the block checkerboard targets are either degenerate or fall within class III solutions. The degenerate class II spin configurations are identified up to a certain block size. We also consider other target spin configurations with different degrees of global symmetries and order. Our investigation reveals that the solution class to which a target belongs depends sensitively on the nature of the target radial spin-spin correlation function. In the future, it will be interesting to explore whether such inverse statistical-mechanical techniques could be employed to design materials with desired spin properties. Publication Date: 1-Oct-2013 Electronic Publication Date: 14-Oct-2013 Citation: DiStasio, Robert A, Marcotte, Étienne, Car, Roberto, Stillinger, Frank H, Torquato, Salvatore. (2013). Designer spin systems via inverse statistical mechanics. Physical Review B, 88 (13), 10.1103/PhysRevB.88.134104 DOI: doi:10.1103/PhysRevB.88.134104 ISSN: 1098-0121 EISSN: 1550-235X Pages: 134104-1 - 134104-14 Type of Material: Journal Article Journal/Proceeding Title: Physical Review B Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.