On the Yang-Lee distribution of roots

Hauge, E. Hiis; Hemmer, P. C.

doi:10.1016/s0031-8914(63)80242-6

Cited by 31 publications

(8 citation statements)

References 4 publications

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“…The unconstrained distribution was first found via its Fourier transform (characteristic function) and its generating cumulants in [40,41] and also analyzed for the box and harmonic traps in [42,43]. In previous works [6,10,39,48,[55][56][57][58] only the first two moments (the mean value and dispersion) were analyzed, with the only exception being [59], where the third moment was discussed. The actual cutoff distribution in equation ( 7) and its explicit relation to the statistics and thermodynamics of an ideal gas was first found and analyzed in [1], while in the later works, including [43], only the auxiliary unconstrained distribution was discussed.…”

mentioning

confidence: 99%

Universal fine structure of the specific heat at the criticalλ-point for an ideal Bose gas in an arbitrary trap

Tarasov¹,

Kocharovsky²

2014

J. Phys. A: Math. Theor.

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We analytically find the universal fine structure of the noted discontinuity in the value and/or derivative of the specific heat of an ideal Bose gas in an arbitrary trap in the whole critical region around the λ-point of the Bose–Einstein condensation. The result reveals a remarkable dependence of the λ-point structure on the trapʼs form and boundary conditions, even for a macroscopically large system. We suggest measuring this strong effect in the experiments with a controllable trap potential.

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mentioning

confidence: 99%

Universal fine structure of the specific heat at the criticalλ-point for an ideal Bose gas in an arbitrary trap

Tarasov¹,

Kocharovsky²

2014

J. Phys. A: Math. Theor.

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“…The pressure may also be expressed as a function of activity z : , P ( z ) = 1 d W 0 ( z d ) where W 0 is the Lambert W-function, defined as the solution x ( z ) to x exp( x ) = z . The density is ρ ( z ) = 1 d W 0 ( z d ) 1 + W 0 ( z d ) The parametric pressure–density relation prescribed by eqs and is identical to that given by eq (pbc boundary).…”

Section: Theorymentioning

confidence: 99%

“…The pressure diverges at ρd = 1, where the rods completely fill the length V. There is no phase transition or other singularity exhibited by the system. The pressure may also be expressed as a function of activity z: 59,60…”

Section: Dnmentioning

confidence: 99%

Origins of the Failure of the Activity Virial Series

Kofke

2023

J. Phys. Chem. B

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We examine the development of the virial equation of state when expressed as a series in the activity with coefficients labeled b n . Using the one-dimensional hard-rod model as a prototype, we consider steps in its development that introduce inaccuracy that leads it to form a divergent series. We discuss the role of volume dependence of the virial coefficients and present expressions and calculations for volume-dependent coefficients b n (V) for the hard-rod model up to n = 200. We examine alternative methods for computing properties from the b n . We recommend that further efforts be made to compute volume-dependent virial coefficients as a means to understand better the virial equation of state and to make it more robust in applications.

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“…In many of these (approximate) extrapolations, the radius of convergence R of the virial expansion is determined by a singularity at some positive value of the density ρ = R, with f ρ ρ > in d = 3 [29][30][31]. This will certainly hold when all B j , or all but a finite number of them, are positive, but need not be 4 Note that the quantity ( )…”

Section: The Virial Expansionmentioning

confidence: 99%

“…The zeros of the grand canonical partition function (GPF) z, ( ) Ξ Λ , of equilibrium systems in a region Λ at fugacity z, continue to be of interest [1] sixty years after their importance for identifying phase transitions was described by Lee and Yang [2,3]. It turns out that in some simple models, the L-Y zeros are confined to the negative half z-plane, or even the negative real z-axis [4][5][6][7][8][9][10]. For example, Heilmann [11] showed that antiferromagnetic Ising models with pair interactions on line graphs (including, e.g.…”

Section: Introductionmentioning

confidence: 99%

A note on Lee–Yang zeros in the negative half-plane

Lebowitz

Scaramazza

2016

J. Phys.: Condens. Matter

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We obtain lower bounds on the inverse compressibility of systems whose Lee-Yang zeros of the grand-canonical partition function lie in the left half of the complex fugacity plane. This includes in particular systems whose zeros lie on the negative real axis such as the monomer-dimer system on a lattice. We also study the virial expansion of the pressure in powers of the density for such systems. We find no direct connection between the positivity of the virial coefficients and the negativity of the L-Y zeros, and provide examples of either one or both properties holding. An explicit calculation of the partition function of the monomer-dimer system on 2 rows shows that there are at most a finite number of negative virial coefficients in this case. * Dedicated to the memory of George Stell

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On the Yang-Lee distribution of roots

Cited by 31 publications

References 4 publications

Universal fine structure of the specific heat at the criticalλ-point for an ideal Bose gas in an arbitrary trap

Universal fine structure of the specific heat at the criticalλ-point for an ideal Bose gas in an arbitrary trap

Origins of the Failure of the Activity Virial Series

A note on Lee–Yang zeros in the negative half-plane

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