Partition function zeros of the Q-state Potts model on the simple-cubic lattice

Kim, Seung‐Yeon

doi:10.1016/s0550-3213(02)00465-0

Cited by 22 publications

(14 citation statements)

References 84 publications

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“…As in the BMH approach, the zero value of t 1 in the limit L → ∞ indicates the existence of a true phase transition. When there is no phase transition, Fisher (or Yang-Lee) edge singularity [39,40] exists if y t > d (or y h > d). As shown in Table I in Table I clearly using Monte Carlo simulation [36].…”

Section: Phase Transitions In Small Systemsmentioning

confidence: 99%

“…As in the BMH approach, the zero value of t 1 in the limit L → ∞ indicates the existence of a true phase transition. When there is no phase transition, Fisher (or Yang-Lee) edge singularity [39,40] been compared for the approximate zeros of quite large (but still small) finite-size systems using Monte Carlo simulation [36]. Here these approaches are compared for the exact zeros of very small finite-size systems (L = 8 to 16).…”

Section: Phase Transitions In Small Systemsmentioning

confidence: 99%

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Density of Yang-Lee zeros for the Ising ferromagnet

Kim

2006

Phys. Rev. E

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The densities of Yang-Lee zeros for the Ising ferromagnet on the L x L square lattice are evaluated from the exact grand partition functions (L=3 approximately 16). The properties of the density of Yang-Lee zeros are discussed as a function of temperature T and system size L. The three different classes of phase transitions for the Ising ferromagnet--first-order phase transition, second-order phase transition, and Yang-Lee edge singularity--are clearly distinguished by estimating the magnetic scaling exponent yh from the densities of zeros for finite-size systems. The divergence of the density of zeros at Yang-Lee edge in high temperatures (Yang-Lee edge singularity), which has been detected only by the series expansion until now for the square-lattice Ising ferromagnet, is obtained from the finite-size data. The identification of the orders of phase transitions in small systems is also discussed using the density of Yang-Lee zeros.

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Section: Phase Transitions In Small Systemsmentioning

confidence: 99%

“…As in the BMH approach, the zero value of t 1 in the limit L → ∞ indicates the existence of a true phase transition. When there is no phase transition, Fisher (or Yang-Lee) edge singularity [39,40] been compared for the approximate zeros of quite large (but still small) finite-size systems using Monte Carlo simulation [36]. Here these approaches are compared for the exact zeros of very small finite-size systems (L = 8 to 16).…”

Section: Phase Transitions In Small Systemsmentioning

confidence: 99%

Density of Yang-Lee zeros for the Ising ferromagnet

Kim

2006

Phys. Rev. E

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“…The exact location of Yang-Lee zeros of the Potts model has attracted attention as we lack the equivalence of the unit circle theorem for this model. Their location has been mostly estimated from finite-size extrapolation 18,58 . An interesting feature of these findings is that for the Potts model for q > 2 the zeros were believed to lie outside the unit circle.…”

Section: Yang-lee Zeros In the Potts Model With A Complex Fieldmentioning

confidence: 99%

“…In three dimensions, previous finite-size study was limited to very small system sizes such as 3 × 3 × 3 58 , but the zeros do not lie on the unit circle. What is their fate in the thermodynamic limit?…”

Section: Yang-lee Zeros In the Potts Model With A Complex Fieldmentioning

confidence: 99%

Density of Yang-Lee zeros in the thermodynamic limit from tensor network methods

García-Sáez

Wei

2015

Phys. Rev. B

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The distribution of Yang-Lee zeros in the ferromagnetic Ising model in both two and three dimensions is studied on the complex field plane directly in the thermodynamic limit via the tensor network methods. The partition function is represented as a contraction of a tensor network and is efficiently evaluated with an iterative tensor renormalization scheme. The free-energy density and the magnetization are computed on the complex field plane. Via the discontinuity of the magnetization, the density of the Yang-Lee zeros is obtained to lie on the unit circle, consistent with the Lee-Yang circle theorem. Distinct features are observed at different temperatures-below, above and at the critical temperature. Application of the tensor-network approach is also made to the q-state Potts models in both two and three dimensions and a previous debate on whether, in the thermodynamic limit, the Yang-Lee zeros lie on a unit circle for q > 2 is resolved: they clearly do not lie on a unit circle except at the zero temperature. For the Potts models (q = 3, 4, 5, 6) investigated in two dimensions, as the temperature is lowered the radius of the zeros at a fixed angle from the real axis shrinks exponentially towards unity with the inverse temperature.

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“…itself and the zeros in the limit T = 0 [19,25,26,27,28]. It has been shown [27,28] that the distributions of the ferromagnetic Yang-Lee zeros for Q > 1 have similar properties independent of dimension.…”

Section: Introductionmentioning

confidence: 99%