Yang-Lee Edge in the High-Temperature Limit

in the complex z = e -2H plane, where H is the reduced external magnetic field. At infinite temperature (T = m) the spins are noninteracting and the partition function reduces to (z 1í2 + z-ìë)~, where N is the total number of spins. The zeros are therefore N-fold degenerate at 8 = a. As the temperature is lowered, the zeros spread into an arc segment of the unit circle centered about 8 = 7r and extending between two Yang-Lee edges at O(T)= ?[A -$A(T)l . The length A(T) of the arc segment grows as the temperature is lowered, eventually reaching A(TC) = 2n (zeros distributed over the whole unit circle) at the critical temperature T,. While the precise expression of A(T) remains unknown4 Kurtze and Fishers have argued from a consideration of the high-temperature series expansion that at high temperatures the gap width behaves as