Yang-Lee edge for the two-dimensional Ising model

Functional renormalization group approach to the Yang-Lee edge singularity

“…In two dimensions the corresponding universality class has been identified with that of the simplest nonunitary conformal field theory (CFT), the minimal model M 2,5 , with central charge c = −22/5 [22]. This allowed to exploit conformal symmetry in two dimensions to calculate the scaling exponent σ(d = 2) = −1/6, which has been confirmed with remarkable accuracy by series expansions [23,24], as well as by comparing arXiv:1605.06039v2 [hep-th] 6 Jul 2016 with experimental high-field magnetization data [7,8]. Furthermore, using integral kernel techniques it is possible to establish the exact result σ(d = 1) = −1/2 [20,21].…”

Density of Yang-Lee zeros for the Ising ferromagnet

“…Kurtze and Fisher [18] refined the estimation of σ by analyzing the high-temperature series expansion for the classical n-vector model and the quantum Heisenberg model in the limit of infinite temperature, and reported σ = −0.163(3) in two dimensions (square and triangular lattices). Baker et al [19] analyzed the series expansion of much greater length for the square-lattice Ising ferromagnet, and obtained σ = −0.1560(33) at y = e −2βJ = 2 3 (T ≈ 5J/k B ) and σ = −0.1576(34) at y = 4 5 (T ≈ 9J/k B ) from integral approximants. Remarkably, the exponent σ has also been experimentally measured to be −0.15 (2) in the range 49K ≤ T ≤ 53K and −0.365 at T = 34K for the triangular-lattice Ising ferromagnet Fisher [20] renamed the edge zero as the Yang-Lee edge singularity for T > T c , and proposed the idea that the Yang-Lee edge singularity can be thought of as a new secondorder phase transition with associated critical exponents.…”

“…The density of Yang-Lee zeros has also been investigated experimentally for the two-dimensional Ising ferromagnet FeCl 2 in axial magnetic fields [14,15]. Until now, the divergence of the density of zeros at Yang-Lee edge (the so-called Yang-Lee edge singularity) for the square-lattice Ising ferromagnet in high temperatures has been obtained only by the series expansion [3,18,19]. Furthermore, for T > T c , the finite-size effects of the density of Yang-Lee zeros for the Ising ferromagnet have never been studied.…”

Synergistic development of differential approximants and the finite lattice method in lattice statistics

“…The FLM has also been used in a number of 'one-off' studies in lattice statistics. For example Baker et al (1986) used high-field series for the square lattice Ising model at specific values of u = z 2 to investigate the distribution of zeroes in the complex μ plane. A special case of general q is the antiferromagnet at zero temperature which gives limit of chromatic polynomials.…”