New mean-field theories for the liquid–vapour transition of charged hard spheres

The phase behaviour of the primitive model of electrolytes is studied in the framework of the various mean-field approximations obtained recently by means of methods pertaining to statistical field theory (J.-M. Caillol, J. statist. Phys., 115, 1461 (2004); extended version: arXiv:cond-mat/0305465). The role of the regularization of the Coulomb potential at short distances is discussed in detail and the link to more traditional approximations of the theory of liquids is discussed. The values computed for the critical temperatures, chemical potentials, and densities are compared with available Monte Carlo data and other theoretical predictions.     

An “observer decomposition” for Everett's theory

Several authors have noted that Everett's theory needs a specification of a special decomposition in order to account for our perceived experience, including quantum measurement results. It is suggested here that a possible way to arrive at such a specification is to relate it to the internal structure of the observer himself.     

Green's function theory of the spin-Peierls transition in X−Y chains

Using a Green's function formalism, we derive from a new microscopic Hamiltonian, the transition temperature equation for the spin-Peierls transition in X−Y quasi-one-dimensional (1D) spin systems. The obtained equation has already been obtained by Beni and Pincus [1] in a different fashion.     

Analyticity of scattering for the ϕ4 theory

We consider scattering for the equation (+m ²)+³=0 on four-dimensional Minkowski space. Form>0, one-to-one and onto wave operatorsW _± :HH are known to exist for all 0, whereH denotes the Hilbert space of finite-energy Cauchy data. We prove that the maps (,u)W _± (u) and (,u)(W _± )^–1 (u) are continuous from [0, )×H toH, and extend to real-analytic functions from an open neighborhood of {0}×H×{0}×H to the Hilbert spaceH _–1 of Cauchy data with Poincaré-invariant norm. Form=0, wave operatorsW _± are known to exist as diffeomorphisms ofH for all 0, where hereH denotes the Hilbert space of finite Einstein energy Cauchy data. In this case we prove that the maps (,u)(W _± ) (u) and (,u)(W _± )^–1 (u) extend to real-analytic functions from a neighborhood of [0, )×H×H toH.     

Comment on “analytic scattering theory for many-body systems below the smallest three-body threshold”

The proof of [1, Lemmas 2.1–2.3] is completed, showing that the operators of multiplication byk ² inH ^t,, |t|1, =0, ±2, have spectrum ⁺ and generate the holomorphic semigroups , Re<0.It is pointed out, that [1, (5.54)] does not hold. Accordingly, a new version of [1, Theorem 5.15] is proved, saying that (5.44) defines an isomorphism of.     

Reply to the Comments of Sharipov on “Symmetry of the Linearized Boltzmann Equation”

This is a reply to the comments by Sharipov on the papers published in J. Stat. Phys. 136:751 (2009) and in J. Stat. Phys. 136:945 (2009). The present reply will show that the comments do not apply to the papers.     

Complete Gauge theory for the whole Poincaré group

Gauge theories for nonsemisimple groups are examined. A theory for the Poincaré group with all the essential characteristics of a Yang-Mills theory necessarily possesses extra equations. Inonü-Wigner contractions of gauge theories are introduced which provide a Lagrangian formalism, equivalent to a Lagrangian de Sitter theory supplemented by weak constraints.Work supported by FINEP under Contract No. B/76/80/146/00/00.Fellow of the CNPq, Brasilia.     

Unconventional large-N limit of the Gaussian effective potential and the phase transition in λφ 4 theory

In the conventional large-N limit the coupling constant is required to scale as 1/N. While the Gaussian effective potential (GEP) is known to contain the exact result in this limit, it shows a phase transition only when 1/N (in units of the renormalized mass in the symmetric vacuum). Here we determine the asymptotic behaviour, asN, of and other quantities at the phase transition of the GEP. We find _crit to be finite in 0+1 dimensions; of order 1/lnN in 1+1 dimensions; 1/N ^1/3 in 2+1 dimensions; and in 3+1 dimensions. The GEP's first-order phase transition is shown to become asymptotically second-order in 1+1 dimensions and below. We also discuss non-integer dimensions and the approach to the non-trivial autonomous theory in 3+1 dimensions.     

Spectral Properties of the Linearized Boltzmann Operator in L p for 1≤p≤∞

The spectrum of both classical and relativistic Boltzmann operator for hard interactions in a whole space is shown to be independent of p in L ^p for 1≤p<∞. It consists of a half-plane $\operatorname{Re} \lambda\leq -\nu_{0}$ and countably many branches in the strip $-\nu_{0}<\operatorname{Re} \lambda \leq0$ . Moreover the resolvent set is independent of p for all 1≤p≤∞ but in L ^∞ this operator possesses in addition to the continuous also an uncountable set of point spectrum.     

“Almost” mean-field ising model: An algebraic approach

We study the thermodynamic limit of the algebraic dynamics for an almost mean-field Ising model, which is a slight generalization of the Ising model in the mean-field approximation. We prove that there exists a family of relevant states on which the algebraic dynamics ^t can be defined. This ^t defines a group of automorphisms of the algebra obtained by completing the standard spin algebra with respect to the quasiuniform topology defined by our states.     

“Conserved charges” of the Bondi-Metzner-Sachs algebra in the Brans-Dicke theory

The asymptotic symmetries in the Brans-Dicke theory are analyzed using Penrose's conformal completion method,which is independent of the coordinate system used.These symmetries,indeed,include supertranslations and Lorentz transformations for an asymptotically flat spacetime.With the Wald-Zoupas formalism,“conserved charges”and fluxes of the Bondi-Metzner-Sachs algebra are computed.The scalar degree of freedom contributes only to the Lorentz boost charge,even though it plays a role in various fluxes.The flux-balance laws are further applied to constrain the displacement memory,spin memory,and center-of-mass memory effects.     

The meaning of the terms “phase” and “phase transition”

Various meanings of the terms phase and phase transition encountered in scientific literature are discussed. These terms supplement each other and cover only together all the macroscopic situations which are now denoted by this term.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 67–71, August, 1988.     

Study of the first-order transition in the spin-1 Blume–Capel model by using effective-field theory

The spin-1 Blume–Capel model on a square lattice is studied by using an effective-field theory (EFT) with correlation. We propose an expression for the free energy within the EFT. The phase diagram is constructed in the temperature (T) and single-ion anisotropy amplitude (D) plane. The first-order transition line is obtained by Maxwell construction (comparison between free energies). Our results predict first-order transitions at low temperatures and large anisotropy strengths, which correspond in the phase diagram to the existence of a tricritical point (TCP). We compare our results with mean-field approximation (MFA), that show a qualitative correct behavior for the phase diagram.