Evidence for phase transitions in finite systems

Miller, H.G.; Cole, B.J.; Quick, R. M.

doi:10.1103/physrevlett.63.1922

Cited by 33 publications

(20 citation statements)

References 17 publications

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“…Despite large fluctuations in the order parameters, which tend to obscure these transitions [16 -18], they can be identified by peaked structures in the specific heat. In canonical ensemble calculations, using either the exact shell model or the experimental nuclear energy eigenspectrum, similar structures are seen in the specific heat which confirms that such shape transitions do occur [21,22,24,25]. Furthermore the critical temperature is predicted remarkably well in FTMF calculations even in small model spaces [26].…”

Section: Introductionsupporting

confidence: 71%

Dependence of nuclear shape transformations on the nuclear volume

Yen

Miller

1994

Phys. Rev. C

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The dependence of nuclear shape transition on changes in the nuclear volume in Mg has been studied within the framework of the constrained Snite temperature Hartree-Fock approximation. The deformation parameters P and p are very sensitive to changes in the nuclear volume. A firstorder shape transition in Mg takes place at the temperature of 1 MeU and at the volume of V, = 1.025 Vo, where Vo is the zero temperature unconstrained volume of the system. Previously we have shown that a 2.570 compression of the system yields a downward shift in the critical temperature of 0.7 MeV. Similarly a 2.5% expansion of the system also yields a decrease in the critical temperature of 0.3 MeV. Finally a compression of the system leads to a corresponding reduction in the magnitude of the level density, while an expansion increases its value only slightly.PACS number(s): 21.60. Jz, 27.30.+t

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Section: Introductionsupporting

confidence: 71%

Dependence of nuclear shape transformations on the nuclear volume

Yen

Miller

1994

Phys. Rev. C

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“…It has been pointed out [1,2] that a peaked structure in the specific heat of a many-body system may be a signature of a "phase transition" or phase transformation. Although in finite quantum systems such peaks are indeed smooth and no sharp transitions are encountered, these peaks are in many cases indicative of significant changes experienced by the system which are due to dynamical effects, and reflect the transitions between different regimes.…”

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confidence: 99%

“…The ensuing expression for the partition function is Z(P) = ) m, exp( -PE, ) + i(n p(E) exp( -PE)dE, (2) where P = I/kT and T is the temperature, i represents the microstates of the system in the s-d shell, I; and E; are the corresponding degeneracy and excitat, ion energy of the ith microstate, and E" is the energy above which the spectrum is replaced by the continuum. In principle the results should not depend on the cutoff energy E" if p(E) correctly represents the density of states.…”

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Dynamical dependence of thermal phase transformations in finite systems

1992

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We examine the dynamical effects in the canonical ensemble calculation of the specific heat of Ne with and without interactions in the s-d shell. Allowing for the inclusion of a continuum as well as a discrete spectrum in both cases, it is seen that the peak in the specific heat is a consequence of the interaction and not a finite size eKect. The same behavior is also observed in other systems.PACS number(s): 21.60.-n, 05.30.-d It has been pointed out [1,2] that a peaked structure in the specific heat of a many-body system may be a signature of a "phase transition" or phase transformation. Although in finite quantum systems such peaks are indeed smooth and no sharp transitions are encountered, these peaks are in many cases indicative of significant changes experienced by the system which are due to dynamical effects, and reflect the transitions between different regimes. In nuclear systems, these peaks can quite generally be understood as signatures of collective to noncollective transitions and can be directly related to abrupt changes in the many-body density of states [3].However, it has recently been argued [4,5] that these peaks may arise from finite size effects (i.e., effects arising only from the truncation of the model space) and are therefore unrelated to the underlying dynamics. Moreover, some type of universality was suggested in this vein [5]. A truncation of the accessible space obviously leads to the vanishing of the specific heat at sufficiently high temperatures which in turn results in a (generally flat) peak in the specific heat at intermediate temperatures.However, we claim that the truncation of the accessible space cannot be held responsible for the peak in the specific heat exhibited by finite nuclei. Moreover, it can be easily seen that the position of these peaks is strongly dependent on the strength of the interaction.In the present work we show first some results obtained in the 8-d shell for the nucleus~Ne with two valence protons and neutrons. We have calculated the specific heat in the canonical ensemble both for the noninteracting system and for the system interacting with a Vary-Yang effective interaction [6], using in both cases the same unperturbed single particle (s.p. ) energies (see Fig. 1). The Vary-Yang interaction in this model space quite accurately describes the lowest part of the experimental spectrum [2]. In order to clearly distinguish the effects of truncation of the model space, we have also included the continuum in both the interacting and nonintcracting systems in the calculation of the specific heat.Let us consider first the calculation in the truncated Permanent address: Department of Physics, University of I a Plata, 1900 La Plata, Argentina. space. In both the interacting and noninteracting cases, two peaks are observed in the specific heat. The lowesttemperature peak is due to the small energy gap between the ground state and the first excited state of the manybody system, in comparison with the energy difference between the ground and second excited st...

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“…As the mass number increases, the low-lying collective portion of the energy spectrum becomes more compressed and an abrupt change in the many particle density of states occurs at lower excitation energies. It has, therefore, been suggested that a collective to non-collective phase transition occurs in finite nuclei [18]. Strictly speaking it is incorrect to speak of phase transitions in finite systems.…”

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confidence: 99%