Convergence of the Mayer Series via Cauchy Majorant Method with Application to the Yukawa Gas in the Region of Collapse

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dc.creatorGuidi, Leonardo F.
dc.creatorMarchetti, Domingos H. U.
dc.date2003-10-14
dc.date2004-05-03
dc.date.accessioned2026-07-07T04:30:39Z
dc.date.available2026-07-07T04:30:39Z
dc.descriptionWe construct majorant functions $Φ(t,z)$ for the Mayer series of pressure satisfying a nonlinear differential equation of first order which can be solved by the method of characteristics. The domain $| z| <(eτ) ^{-1}$ of convergence of Mayer series is given by the envelop of characteristic intersections. For non negative potentials we derive an explicit solution in terms of the Lambert $W$ --function which is related to the exponential generating function $T$ of rooted trees as $T(x)=-W(-x)$. For stable potentials the solution is majorized by a non negative potential solution. There are many choices in this case and we combine this freedom together with a Lagrange multiplier to examine the Yukawa gas in the region of collapse. We give, in this paper, a sufficient condition to establish a conjecture of Benfatto, Gallavotti and Nicoló. For any $β\in \lbrack 4π, 8π)$, the Mayer series with the leading terms of the expansion omitted (how many depending on $β$) is shown to be convergent provided an improved stability condition holds. Numerical calculations presented indicate this condition is satisfied if few particles are involved.
dc.descriptionEmails: guidi@if.usp.br and marchett@if.usp.br
dc.identifierhttps://arxiv.org/abs/math-ph/0310025
dc.identifierhttp://arxiv.org/abs/math-ph/0310025
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57533
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subjectGeneral Topology
dc.subject82B05;82B28;35F25
dc.titleConvergence of the Mayer Series via Cauchy Majorant Method with Application to the Yukawa Gas in the Region of Collapse
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