V Matveev and R Shrock 1995 J. Phys. A: Math. Gen. 28 4859 doi:10.1088/0305-4470/28/17/018
V Matveev and R Shrock
Show affiliationsWe study the complex-temperature properties of a rare example of a statistical mechanical model which is exactly solvable in an external symmetry-breaking field, namely, the Ising model on the square lattice with beta H=+or-i pi /2. This model was solved by Lee and Yang (1952). We first determine the complex-temperature phases and their boundaries. From a low-temperature, high-field series expansion of the partition function, we extract the low-temperature series for the susceptibility chi to O(u23), where u=e-4K. Analysing this series, we conclude that chi has divergent singularities (i) at u=u3=-(3-232/) with exponent gamma e'=5/4, (ii) at u=1, with exponent gamma 1'=5/2, and (iii) at u=us=-1, with exponent gamma s'=1. We also extract a shorter series for the staggered susceptibility and investigate its singularities. Using the exact result of Lee and Yang for the free energy, we calculate the specific heat and determine its complex-temperature singularities. We also carry this out for the uniform and staggered magnetization.
75.10.Hk Classical spin models
75.30.Cr Saturation moments and magnetic susceptibilities
05.70.Ce Thermodynamic functions and equations of state
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects
82B30 Statistical thermodynamics (See also 80-XX)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Issue 17 (7 September 1995)
V Matveev and R Shrock 1995 J. Phys. A: Math. Gen. 28 4859
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