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On Properties of the Ising Model for Complex Energy/Temperature and Magnetic Field | | Victor Matveev
; Robert Shrock
; | | Date: |
29 Nov 2007 | | Abstract: | We study some properties of the Ising model in the plane of the complex
(energy/temperature)-dependent variable $u=e^{-4K}$, where $K=J/(k_BT)$, for
nonzero external magnetic field, $H$. Exact results are given for the phase
diagram in the $u$ plane for the model in one dimension and on infinite-length
quasi-one-dimensional strips. In the case of real $h=H/(k_BT)$, these results
provide new insights into features of our earlier study of this case. We also
consider complex $h=H/(k_BT)$ and $mu=e^{-2h}$. Calculations of complex-$u$
zeros of the partition function on sections of the square lattice are
presented. For the case of imaginary $h$, i.e., $mu=e^{i heta}$, we use exact
results for the quasi-1D strips together with these partition function zeros
for the model in 2D to infer some properties of the resultant phase diagram in
the $u$ plane. We find that in this case, the phase boundary ${cal B}_u$
contains a real line segment extending through part of the physical
ferromagnetic interval $0 le u le 1$, with a right-hand endpoint $u_{rhe}$ at
the temperature for which the Yang-Lee edge singularity occurs at $mu=e^{pm
i heta}$. Conformal field theory arguments are used to relate the
singularities at $u_{rhe}$ and the Yang-Lee edge. | | Source: | arXiv, 0711.4639 | | Services: | Forum | Review | PDF | Favorites | |
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