Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-05-19
Phys. Rev. B 84, 094439 (2011)
Physics
Condensed Matter
Statistical Mechanics
9 pages, 7 figures, revised and expanded, published version
Scientific paper
10.1103/PhysRevB.84.094439
We develop a fully microscopic, statistical mechanics approach to study phase transitions in Ising systems with competing interactions at different scales. Our aim is to consider orientational and positional order parameters in a unified framework. In this work we consider two dimensional stripe forming systems, where nematic, smectic and crystal phases are possible. We introduce a nematic order parameter in a lattice, which measures orientational order of interfaces. We develop a mean field approach which leads to a free energy which is a function of both the magnetization (density) and the orientational (nematic) order parameters. Self-consistent equations for the order parameters are obtained and the solutions are described for a particular system, the Dipolar Frustrated Ising Ferromagnet. We show that this system has an Ising-nematic phase at low temperatures in the square lattice, where positional order (staggered magnetization) is zero. At lower temperatures a crystal-stripe phase may appear. In the continuum limit the present approach connects to a Ginsburg-Landau theory, which has an isotropic-nematic phase transition with breaking of a continuous symmetry.
Barci Daniel G.
Stariolo Daniel A.
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