Geometric transitions

The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in mathematics and in physics.     

Phase transitions in the Ashkin-Teller model

For some values of the coupling constants, a proof of the existence of two phase transitions in the Ashkin-Teller model is given. Only correlation inequalities are used.     

Multiphoton transitions for the harmonic oscillator

2- and 3-photon electric dipole transitions for the harmonic oscillator are shown to have zero intensity. This is extended to the general cases of Δv?=?n and Δv?=?n???2 for n-photon transitions. Although not proved in general, it seems likely that all multiphoton transition moments vanish. This suggests that electric dipole multiphoton transition intensity is due to anharmonicity.     

Folding transitions of the square-diagonal lattice

We address the problem of “phantom” folding of the tethered membrane modeled by the two-dimensional square lattice, with bonds on the edges and diagonals of each face. Introducing bending rigidities K₁ and K₂ for respectively long and short bonds, we derive the complete phase diagram of the model, using transfer matrix calculations. The latter displays two transition curves, one corresponding to a first-order (ferromagnetic) folding transition, and the other to a continuous (anti-ferromagnetic) unfolding transition.     

Spin polarization transitions in the FQHE

The spin polarization of the FQHE ground states at fixed filling factors is analyzed within a composite fermion model. As a function of the perpendicular magnetic field several cross‐overs between differently polarized ground states are predicted, in agreement with recent experimental investigations. The magnetic field and temperature scalings of the polarization, as well as the magnetic field dependence of the spin‐flip gap are studied.     

Bound-free transitions and the dissociation limit

Following a sequential two-photon excitation, fluorescence is observed from several selectively excited single rotational-vibrational energy levels of theE ³ π0 _g ⁺ state of molecular iodine. The re-emittedE →B fluorescence spectrum from each of the populated rovibrational level of theE state consists of a series of sharp lines terminating on the various discrete ro-vibrational levels of theB state and a few broad lines due to transitions taking place on to the continuum of theB state. The point of transition from sharp lines to broad features in the fluorescence spectrum has been utilized to determine theB state dissociation limit. This method of obtaining the dissociation limit of the molecular electronic states appears to be quite simple and straightforward.     

Phase transitions in the frustration network

The distribution of the frustrated plaquettes is calculated as a function of disorder for two and three dimensional random Ising- andXY-models. It is shown that in all cases the frustrated plaquettes are highly correlated and that at a critical value of disorder a phase transition occurs in the frustration network which can be viewed as a dissociation of plaquettes. The critical disorder is calculated using duality transformations. We show that in the two and three dimensional random Ising systems two types of nonmagnetic phases exist which differ qualitatively by their distribution of frustrated plaquettes and consequently by their domain wall structure.     

Unusual spin transitions

New heterospin complexes of Cu(hfac)₂ (hfac, hexafluoroacetylacetonate) with pyrazole-substituted nitronyl nitroxides have been found that in the solid state exhibit thermally induced spin transitions analogous to spin crossover. For the first complex, [Cu(hfac)₂L^i-Pr], at room temperature, the Cu—O_L distances, where O_L is the oxygen atom of the nitroxyl group, are very short (2.143 Å). This leads to a strong antiferromagnetic exchange (～-120cm^?1) in the > N—^·O—Cu²⁺—O^·—N < exchange clusters. The CuO₆ coordination units formed by four O atoms of the two hfac anions and by the nitroxyl O atoms of the two bridging nitroxides have a rare form of flattened octahedra, transformed at low temperatures into elongated octahedra with shorter Cu—O_L distances (2.143 Å→2.002Å) and two longer Cu—O_hfac distances (2.130 Å→2.293 Å). For the second complex, [Cu(hfac)₂L^Bu·0.5C₆H₁₄], unusual low temperature structural dynamics of heterospin systems have been found. It is characterized by the formation of two types of CuO₆ unit. The axial Cu—O_L distances are lengthened in one unit (2.250 Å→2.347 Å) and shortened in the other (2.250 Å → 2.006 Å). This leads to a sophisticated μ_eff(T) dependence with μ_eff drastically decreased at 163 K as a result of full coupling of two spins in half of all >N—^·O—Cu²⁺—O^·—N < exchange clusters and to a shift from antiferromagnetic to ferromagnetic exchange in the other half.     

Cosmic phase transitions

The sequence of phase transitions during the hot history of the universe is followed within a phenomenological framework. Particular emphasis is put on the QCD confinement transition, which is at reach under earth laboratory conditions. A tepid inflationary scenario on the GUT scale with bubble growth at moderate supercooling is discussed.     

量子相变

量子相变是一种发生在绝对零度,由量子涨落而非热涨落导致的相变现象,满足著名的海森堡不确定关系。通过零温量子临界点的研究,可获知物质系统更广泛范围的行为,包括稀土磁性绝缘体,高温超导体和二维电子气体等。     

Holographic Roberge-Weiss transitions

We investigate \( \mathcal{N} = 4 \) SYM coupled to fundamental flavours at nonzero imaginary quark chemical potential in the strong coupling and large N limit, using gauge/gravity duality applied to the D3-D7 system, treating flavours in the probe approximation. The interplay between \( {\mathbb{Z}_N} \) symmetry and the imaginary chemical potential yields a series of first-order Roberge-Weiss transitions. An additional thermal transition separates phases where quarks are bound/ unbound into mesons. This results in a set of Roberge-Weiss endpoints: we establish that these are triple points, determine the Roberge-Weiss temperature, give the curvature of the phase boundaries and confirm that the theory is analytic in μ ² when μ ² ≈ 0.     

Kinetic depinning transitions

A simple model for the kinetics of two interacting interfaces moving at a prescribed rate is proposed. It is a kinetic generalization for problems like wetting, pinning, surface-segregation or surface-reordering during solidification. Various types of nonequilibrium phase-transitions are predicted.     

Intramolecular non-radiative transitions

Non-radiative electronic transitions are discussed. The probability W_i of the electron staying in the initial state i is obtained as a function of the vibrational relaxation time, in both large and small molecules. The result at low temperature is

where ε is the vibrational relaxation rate, ?ωm' is the energy difference of the levels which are involved in the transitions. An expression which depends on the phonon temperature is also obtained.     

On the order of itinerant antiferromagnetic phase transitions and superconducting phase transitions in an exchange field

The coefficients of the second and fourth order terms in a Landau expansion of the free energy are evaluated for an itinerant antiferromagnetic transition. The choice of spatial dependence is found to play an important role. A first order transition is obtained for a range of values of the band structure parameters. However if values appropriate to Cr are used it is found that the contribution from the shift in the Fermi level is sufficiently large to give second order transitions even when magnetostrictive effects are included. In the mathematically similar problem of a superconductor in an exchange field it is found that the transition from normal to superconducting states is first order near the triple point with an upper and possibly a lower critical point where the transition changes to second order.