Methods of the theory of singularities in the phenomenology of phase transitions

Kut’in, E.I.; Lorman, Vladimir; Павлов, С. Д.

doi:10.1070/pu1991v034n06abeh002385

Cited by 37 publications

(31 citation statements)

References 8 publications

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“…An example of a coupled model with linear-quadratic coupling occurs in the context of isostructural transitions [20]. It is conceivable that in some cases a linear-cubic coupling may be symmetry allowed.…”

Section: Discussionmentioning

confidence: 99%

Domain wall and periodic solutions of a coupled ϕ6 model

Khare

Saxena

2008

Journal of Mathematical Physics

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Abstract:We obtain several higher order periodic solutions of a Coupled φ 6 model in terms of Lamé polynomials of order one and two. These solutions are unusual in the sense that while they are the solutions of the coupled problem, they are not the solutions of the uncoupled problem. We also obtain exact solutions of coupled φ 6 -φ 4 models, both when the φ 4 potential corresponds to a first order (asymmetric double well) or a second order (symmetric double well) transition.

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Section: Discussionmentioning

confidence: 99%

Domain wall and periodic solutions of a coupled ϕ6 model

Khare

Saxena

2008

Journal of Mathematical Physics

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“…The most simple phase diagram presenting stability regions for all four phases can be calculated by using the following truncated free energy [30]:…”

Section: Phase Diagrams and Modulated Structuresmentioning

confidence: 99%

Theory of chiral periodic mesophases formed from an achiral liquid of bent-core molecules

Lorman

Mettout²

2004

Phys. Rev. E

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The theory of unconventional one-dimensional periodic mesophases forming in a liquid of achiral bent-core molecules is presented. The order parameter is a polarization wave. Three distinct phases which can be stabilized directly from the isotropic liquid phase are associated with linear, circular, and elliptic polarizations of the wave. The elliptic polarization leads to the structure of the commonly studied B2 "bent-core" mesophase whereas the recently discovered C(p) phase may be assigned to the linear polarization. We present the molecular configurations and macroscopic properties of the stable states. Their behavior under chiral doping and electric field application are investigated and the corresponding phase diagrams are calculated.

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“…9, is drawn in the space of the free-energy coefficients. In order that the theoretical phase diagram reflects the experimental phase diagram, one has to follow precise rules, deduced from the theory of Singularities [12], for determining the coefficients varying with external variables (T , P , x, ...) and the form of their dependence on the external variables. 1) The number of varying coefficients should be equal to the number of external variables, i.e., one-two-or-three dimensional phase diagrams require a dependence of one-two-or-three coefficients, respectively, on the external variables.…”

Section: Dependence Of the Phenomenological Coefficients On External mentioning

confidence: 99%

Extensions and some recent applications of the Landau theory of phase transitions

Tolédano

2012

EPJ Web of Conferences

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The basic concepts of the Landau theory of phase transitions are introduced through working examples. A number of rules governing the application of the theory to second and first-order transitions are given. The approach to magnetostructural transitions in magnetic mulltiferroic materials is detailed. Examples of transitions induced by replica of the same order-parameter in superconducting and liquid crystal systems, are described. The theory of reconstructive transitions is outlined and illustrated by the examples of the graphite-diamond transition and by the phase diagram of iron. An extention of the phenomenological approach to incommensurate structures to the crystal-amorphous transition is proposed (see also the chapter by Perez-Mato et al. for further discussion and applications).

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Methods of the theory of singularities in the phenomenology of phase transitions

Cited by 37 publications

References 8 publications

Domain wall and periodic solutions of a coupled ϕ6 model

Domain wall and periodic solutions of a coupled ϕ6 model

Theory of chiral periodic mesophases formed from an achiral liquid of bent-core molecules

Extensions and some recent applications of the Landau theory of phase transitions

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