Topologically correct phase boundaries and transition temperatures for Ising Hamiltonians via self-consistent coarse-grained cluster-lattice models

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2011-04-01
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Tan, Teck
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Johnson, Duane
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Ames National Laboratory

Ames National Laboratory is a government-owned, contractor-operated national laboratory of the U.S. Department of Energy (DOE), operated by and located on the campus of Iowa State University in Ames, Iowa.

For more than 70 years, the Ames National Laboratory has successfully partnered with Iowa State University, and is unique among the 17 DOE laboratories in that it is physically located on the campus of a major research university. Many of the scientists and administrators at the Laboratory also hold faculty positions at the University and the Laboratory has access to both undergraduate and graduate student talent.

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We derive a cluster mean-field theory for an Ising Hamiltonian using a cluster-lattice Fourier transform with a cluster of size Nc and a coarse-grained (CG) lattice into cells of size Ncell. We explore forms with Ncell⩾Nc, including a non-CG (NCG) version with Ncell→∞. For Nc=Ncell, the set of static, self-consistent equations relating cluster and CG lattice correlations is analogous to that in dynamical cluster approximation and cellular dynamical mean-field theory used in correlated electron physics. A variational Nc-site cluster grand potential based on Nc=Ncell CG lattice maintains thermodynamic consistency and improves predictions, recovering Monte Carlo and series expansion results upon finite-size scaling; notably, the Nc=1 CG results already predict well the first- and second-order phase boundary topology and transition temperatures for frustrated lattices. The NCG version is significantly faster computationally than the CG case and more accurate at fixed Nc for ferromagnetism, which is potentially useful for cluster expansion and quantum cluster applications.

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This article is from Phys. Rev. B 83, 144427 (2011), doi:10.1103/PhysRevB.83.144427. Posted with permission.

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Sat Jan 01 00:00:00 UTC 2011
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