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1.
The topological hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the configuration space of the short range Berlin-Kac spherical model, for spins lying in hypercubic lattices of dimension d. We find a continuum of changes in the topology and also a finite number of discontinuities in some topological functions. We show, however, that these discontinuities do not coincide with the phase transitions which happen for d > or = 3, and conversely, that no topological discontinuity can be associated with them. This is the first short range, confining potential for which the existence of special topological changes are shown not to be sufficient to infer the occurrence of a phase transition.  相似文献   

2.
We characterize the topology of the phase space of the Berlin-Kac spherical model in the context of the so called Topological Hypothesis, for spins lying in hypercubic lattices of dimension d. For zero external field we are able to characterize the topology exactly, up to homology. We find that, even though there is a continuum of changes in the topology of the corresponding manifolds, for d ≥ 3 there are abrupt discontinuities in some topological functions that could be good candidates to associate with the phase transitions that occur at the thermodynamic level. We show however that these changes do not coincide with the phase transitions and conversely, that no topological discontinuity can be associated to the points where the phase transitions take place. At variance with what happens in the Mean Field version of this same model, we show that these abrupt topological changes are accessible thermodynamically. We conclude that, even in short range systems, the topological mechanism does not seem to be responsible for the triggering of a phase transition. We also analyze the case of spins connected to a macroscopic number of (but not all) neighbors, and find that, similar to the results found for the fully connected version, in this case the topological hypothesis seems to hold: the phase transition coincides with an accumulation point of the topological changes present in configuration space. The question of the ensemble equivalence in the short range spherical model is also considered.  相似文献   

3.
The relation between thermodynamic phase transitions in classical systems and topology changes in their configuration space is discussed for a one-dimensional, analytically tractable solid-on-solid model. The topology of a certain family of submanifolds of configuration space is investigated, corroborating the hypothesis that, in general, a change of the topology within this family is a necessary condition in order to observe a phase transition. Considering two slightly differing versions of this solid-on-solid model, one showing a phase transition in the thermodynamic limit and the other not, we find that the difference in the quality or strength of this topology change appears to be insignificant. This example indicates the unattainability of a condition of exclusively topological nature which is sufficient to guarantee the occurrence of a phase transition in systems with nonconfining potentials.  相似文献   

4.
We report upon the numerical computation of the Euler characteristic chi (a topologic invariant) of the equipotential hypersurfaces Sigma(v) of the configuration space of the two-dimensional lattice varphi(4) model. The pattern chi(Sigma(v)) versus v (potential energy) reveals that a major topology change in the family Sigma(v)(vinR) is at the origin of the phase transition in the model considered. The direct evidence given here-of the relevance of topology for phase transitions-is obtained through a general method that can be applied to any other model.  相似文献   

5.
A most popular model in the family of two-dimensional uniformly-frustratedXY models is the antiferromagnetic model on a triangular lattice [AFXY(t) model]. Its ground state is both continuously and twofold discretely degenerated. Different phase transitions possible in such systems are investigated. Relevant topological excitations are analyzed and a new class of such (vortices with a fractional number of circulation quanta) is discovered. Their role in determining the properties of the system proves itself essential. The characteristics of phase transitions related to breaking of discrete and continuous symmetries change. The phase diagram of the generalized AFXY(t) model is constructed. The results obtained are rederived in the representation of the Coulomb gas with half-integer charges, equivalent to the AFXY(t) model with the Berezinskii-Villain interaction.  相似文献   

6.
We consider the branching and annihilating random walk and with reaction rates σ and λ, respectively, and hopping rate D, and study the phase diagram in the λ/D,σ/D) plane. According to standard mean-field theory, this system is in an active state for all σ/D≥0, and perturbative renormalization suggests that this mean-field result is valid for d>2; however, nonperturbative renormalization predicts that for all d there is a phase transition line to an absorbing state in the λ/D,σ/D) plane. We show here that a simple single-site approximationreproduces with minimal effort the nonperturbative phase diagram both qualitatively and quantitatively for all dimensions d>2. We expect the approach to be useful for other reaction-diffusion processes involving absorbing state transitions.  相似文献   

7.
《Physica A》2006,365(1):128-131
Two mathematical mechanisms, responsible for the generation of a thermodynamic singularity, are individuated. For a class of short-range, confining potentials, a topology change in some family of configuration space submanifolds is the only possible such mechanism. Two examples of systems in which the phase transition is not accompanied by a such topology change are discussed. The first one is a model with long-range interactions, namely the mean-field ϕ4-model, the second example is a one-dimensional system with a non-confining potential energy function. For both these systems, the thermodynamic singularity is generated by a maximization over one variable (or one discrete index) of a smooth function, although the context in which the maximization occurs is very different.  相似文献   

8.
In this paper we study the ground state phase diagram of a one-dimensional t-U-J model, at half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy, a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With reduction of the bandwidth, a transition into an insulating phase showing properties of the spin- XY model takes place.Received: 6 February 2004, Published online: 9 April 2004PACS: 71.10.Hf Non-Fermi-liquid ground states, electron phase diagrams and phase transitions in model systems - 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 74.20.Mn Nonconventional mechanisms (spin fluctuations, polarons and bipolarons, resonating valence bond model, anyon mechanism, marginal Fermi liquid, Luttinger liquid, etc.) - 71.27. + a Strongly correlated electron systems; heavy fermions - 75.10.Pq Spin chain modelsG.I. Japaridze: Permanent address: Andronikashvili Institute of Physics, Georgian Academy, Tamarashvili 6, Tbilisi 380077, Georgia  相似文献   

9.
The self-energy-functional approach proposed recently is applied to the single-band Hubbard model at half-filling to study the Mott-Hubbard metal-insulator transition within the most simple but non-trivial approximation. This leads to a mean-field approach which is interesting conceptually: Trial self-energies from a two-site single-impurity Anderson model are used to evaluate an exact and general variational principle. While this restriction of the domain of the functional represents a strong approximation, the approach is still thermodynamically consistent by construction and represents a conceptual improvement of the linearized DMFT which has been suggested previously as a handy approach to study the critical regime close to the transition. It turns out that the two-site approximation is able to reproduce the complete (zero and finite-temperature) phase diagram for the Mott transition. For the critical point at T = 0, the entire calculation can be done analytically. This calculation elucidates different general aspects of the self-energy-functional theory. Furthermore, it is shown how to deal with a number of technical difficulties which appear when the self-energy functional is evaluated in practice.Received: 3 November 2003, Published online: 23 December 2003PACS: 71.10.-w Theories and models of many-electron systems - 71.15.-m Methods of electronic structure calculations - 71.30. + h Metal-insulator transitions and other electronic transitions  相似文献   

10.
For two-dimensional uniformly frustratedXY models the group of symmetry spontaneously broken in the ground state is a cross product of the group of two-dimensional rotations by some discrete group of finite order. Different possibilities of phase transitions in such systems are investigated. The transition to the Coulomb gas with noninteger charges is widely used when analyzing the properties of relevant topological excitations. The number of these excitations includes not only domain walls and traditional (integer) vortices, but also vortices with a fractional number of circulation quanta which are to be localized at bends and intersections of domain walls. The types of possible phase transitions prove to be dependent on their relative sequence: in the case the vanishing of domain wall free energy occurs earlier (at increasing temperature) than the dissociation of pairs of ordinary vortices, the second phase transition is to be associated with dissociation of pairs of fractional vortices. The general statements are illustrated with a number of examples.  相似文献   

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