First-order Transition Line Research Articles

Cayley-tree Ising model with antiferromagnetic nearest-neighbor and ferromagnetic equivalent-neighbor interactions.

The phase diagram of the Ising model with antiferromagnetic nearest-neighbor interactions and ferromagnetic equivalent-neighbor interactions on the Cayley tree is determined exactly. A nonuniversal critical line separates the disordered and the ordered phases. A line of first-order transitions separating ferromagnetic order from antiferromagnetic order ends in the midst of the ordered phase at a classical ordered critical point. For a small range of values of the ratio of the two couplings, two transitions occur as the temperature is varied. In this case the uniform magnetization is not a monotonic function of the temperature.

Multicritical point in the magnetic phase diagram of CsNiCl3 (abstract)

A previously developed1 Landau-type free-energy functional forms the basis of a theory for the low-temperature magnetic properties of CsNiCl3 under the influence of an applied magnetic field. Three magnetically ordered phases, as well as the paramagnetic phase, are found to all coexist at a single multicritical point representing the intersection of one line of first-order phase transitions and three lines of second-order transitions in the H-T diagram. The temperature dependencies of the critical fields are in good agreement with corresponding experimental data.2

Monte Carlo simulations of SU(2) lattice gauge theories at different space time dimensions

We present the first results of an analysis on the influence of the space-time dimesionality in SU(2) lattice gauge theories with mixed actions. In four dimensions, we clarify the relations between the lines of first-order transitions and the quasi-singular behavior in the cross-over region of the Wilson action. In d = 5 we found that the phase transition that appears in the Wilson action does not separate two distinct phases. The 3-d case and the nature of these phase transitions are also discussed.

High magnetic field study of the normal spinel MnV/sub 2/O/sub 4/

Detailed magnetization measurements are performed up to H=110 kOe in the temperature range 4.2 K<T<70 K on the ferrimagnetic normal spinel MnV/sub 2/O/sub 4/ (T/sub c/ approximately=56 K). In the (M, T) plane, all isofield curves display hysteresis loops which are located between two temperatures T/sub a/ (H/sub i/) and T/sub A/" (H/sub i/), increasing with H/sub i/. From these T/sub a/ and T'/sub a/ values, a (H, T) phase diagram is derived, delimitating five magnetic regions, which is in excellent agreement with the set of isotherm magnetization curves. It is assumed that both T/sub a/ (H) and T'/sub a/ (H) are first-order transition lines, the increased stability of the triangular configuration with H being discussed in terms of a large spin-orbit coupling of the V/sup 3+/ magnetic moments.<<ETX>>

Cylindrical domain structure in metamagnets and its stability conditions

The possibility of the existence of a cylindrical magnetic domain structure near the first-order phase transition line is investigated theoretically in metamagnets, compounds with anisotropy energy substantially exceeding the exchange interaction energy. The domain structure of such compounds is related to the kinetics of the transition from the paramagnetic to the antiferromagnetic state. The static properties of isolated cylindrical magnetic domains and their equilibrium lattices are studied using an energetic approach. It is shown that for a low-temperature metamagnetic phase transition domains of the existence of a cylindrical domain structure, lattices and isolated cylindrical magnetic domains, abut, on the domain of plane-parallel domain structure existence from both sides. The features of their behavior are determined as a function of the magnitude of the external magnetic fields.

New critical point in smectic liquid crystals.

We study a new critical point which terminates a first-order transition line along which two smectic-A (SmA) liquid-crystal phases (or more generally any layered phases with uniaxial symmetry) with different layer spacing coexist. We call this new critical point C the SmA-SmA' critical point. We develop a model nonlinear elastic Hamiltonian to describe physical properties in the vicinity of C. We study this model using mean-field theory, one-loop-order perturbation theory, and the \ensuremath{\epsilon} expansion. In mean-field theory, the SmA-SmA' transition is identical to the mean-field liquid-gas transition. In one-loop perturbation theory, critical corrections to the compressibility become important below an upper critical dimension of 6. In addition, there are important critical corrections to third-order vertex function between 6 and 8 dimensions indicating deviations from mean-field behavior below 8 dimensions. We determine a fixed point in 6-\ensuremath{\epsilon} dimensions describing C and calculate critical exponents to the first order in \ensuremath{\epsilon}. This fixed point exhibits anisotropic scaling with different correlation length exponents ${\ensuremath{\nu}}_{?}$ and ${\ensuremath{\nu}}_{\ensuremath{\perp}}$ parallel and perpendicular to the director. Scaling properties and x-ray scattering patterns in the vicinity of the SmA-SmA' critical point are also considered.

Multicritical point in the magnetic phase diagram of CsNiCl3.

A phenomenological Landau-type free energy forms the basis of a theory for the low-temperature magnetic properties of CsNi${\mathrm{Cl}}_{3}$ under the influence of an applied magnetic field. Three magnetically ordered phases, as well as the paramagnetic phase, are found to coexist at a novel type of multicritical point representing the intersection of one line of first-order transitions and three lines of second-order transitions in the $H\ensuremath{-}T$ phase diagram. The temperature dependences of the critical fields are in good agreement with corresponding experimental data. Similar results are predicted for CsNi${\mathrm{Br}}_{3}$.

Tricritical behaviour in lamellar phases

The author presents a theoretical study of the stability, unbinding and phase separation of lyotropic smectic liquid crystals. The complex interplay between the bare interactions, namely the van der Waals, hydration or electrostatic forces, and membrane fluctuations is analysed and discussed within a linear functional renormalisation group (FRG). Tricritical behaviour is found, dependent on the two parameters epsilon =(kT-W)/kT, where W is a Hamaker constant, and lambda , which describes the resistance to membrane overlap. For lambda &lt;0 (strong exclusion forces), the unbinding transition first predicted by Lipowsky and Leibler (1986) with a mean spacing z diverging as z approximately (- epsilon )-1 is recovered. For lambda &gt;0 (soft membranes), a line of first-order transitions between a finite z system and a phase of isolated membranes (z= infinity ) is found. The existence of particles unable to enter the smectic phase induces an osmotic pressure which leads to the existence of two coexisting lamellar phases, with largely different spacings z1 and z2&gt;&gt;z1.

Z2Abelian Higgs: a cluster expansion approach

The Z2 lattice Abelian Higgs model in D=2+1 is studied. New cluster expansion techniques which involve consideration of two perturbative terms are developed. These are used to obtain strong coupling expansions, for the vacuum energy density and the mass gaps of both 'meson' and 'plaquette' excitations. The expansions are used, via Pade approximant techniques and duality considerations, to explore the phase diagram of the theory. The location of the second-order phase boundaries are in good agreement with those obtained by other methods. The behaviour of the line of first-order transitions is examined and is estimated to terminate at lambda >or approximately=4.5.

Phase diagrams of the q-state potts model on Bethe lattices

We use a rigorous, recently developed, method of solution of spin models on Bethe lattices (Cayley trees). It allows us to detect all the phases of the ferromagnetic and antiferromagnetic q-state Potts models in a field (FPM and APM respectively). The phase diagrams of the FPM are characterized by three critical lines of first-order transitions. In the APM the ordered phases (which appear always for h > 0, and under certain conditions for h= 0 and/or h<0) are separated from the disordered one by phase boundaries characterized by second-order transitions, and are separated one from the other by critical lines characterized by first-order and second-order transitions. Several results are found, which hold true on standard lattices, too.

The SU( N) lattice Higgs model at strong gauge coupling

A family of lattice Higgs models with matter fields carrying the fundamental representation of an SU( N) gauge group is analyzed at strong gauge coupling. Similarities with QCD with staggered fermions are emphasized. For large N the phase diagram is derived, and the scaling limit at the critical endpoint of the first-order Higgs-confinement transition line is investigated.

Monopoles and specific heat in SU(2) lattice gauge theory with a mixed action

Using Monte Carlo simulations, the density of Z(2) monopoles and the value of the specific heat have been measured in SU(2) lattice gauge theory with an action mixture of the fundamental and adjoint representations. A sharp peak in the specific heat has been observed along points lying on a straight line which stretches from the end-point of the first-order transition line. There has also been detected an abrupt decrease of the monopole density on this line. All these results show a strong correlation between the singular behaviour in the cross-over region of the Wilson action and the phase transition structure of the mixed fundamental-adjoint SU(2) theory.

Field effects and the critical end point in polymeric nematics

We calculate the effect of an external field on nematic polymer liquid crystals with polarizable dipoles along the chain backbone. In close analogy to conventional nematics we find a line of first-order transitions from nematic to paranematic as the field is increased, culminating in a critical end point as the critical field is attained. This critical point is related to those found by other authors. The results hold for electric and magnetic fields, the latter coupling to diamagnetic anisotropy. The electric case will be complicated if permanent dipoles are present. We demonstrate the equivalence of these results to the Landau approach in a field. Shortcomings in previous work on nematic polymers in fields are analysed.

Deconfinement and chiral-symmetry restoration in finite-temperature lattice QCD.

Using a mean-field method we obtain some qualitative results regarding the phase diagram of this theory. Emphasis is given to the interdependence between chiral-symmetry restoration and deconfinement. For the coupling constant below a given value, where what is left of deconfinement penetrates enough into the broken-chiral-symmetry phase, we find a line of first-order phase transitions even for vanishing bare-quark mass.

Three-spin interaction Ising model with a nondegenerate ground state at zero applied field

The field-temperature phase diagram of a two-dimensional, three-spin interaction Ising model is studied using two different methods: mean field approximation and numerical transfer matrix techniques. The former leads to a rather rich phase diagram in which two separate phases with different symmetries can be found, and which presents first-order transition lines, a triple point, and a critical end point, like the solid-liquid-gas phase diagram of a pure compound. The numerical transfer matrix study confirms part of these results, but does not clearly evidence the existence of the less symmetric phase.

Tricritical points in three-dimensional XY model with mixed action.

We present theoretical arguments (using mean fields and strong-coupling graphs) for a line of first-order phase transitions in the three-dimensional $\mathrm{XY}$ model with the mixed action $\ensuremath{\beta}cos({\ensuremath{\nabla}}_{i}\ensuremath{\theta})+\ensuremath{\gamma}cos(2{\ensuremath{\nabla}}_{i}\ensuremath{\theta})$, where $\ensuremath{\gamma}\ensuremath{\in}(0.35,0.40)$, and verify its existence by a Monte Carlo simulation.

Competition of Peierls instabilities induced by band-structure effects in quasi-one-dimensional conductors

The author presents a simple mean-field theory describing the mechanism for a Peierls distortion in quasi-one-dimensional conductors whose band structure consists of two bands crossing the Fermi level at two different wave-vectors. He stresses that the electron-phonon coupling may have (g3 not=0) or not have (g3=0), depending upon the symmetry of the two bands and the nature of the soft phonon, a term that connects the two bands. The second case is thoroughly studied and shown to have a phase diagram presenting a second-order transition line between an undistorted phase and a (semi-)metallic Peierls state with a sliding wave-vector, and a first-order transition line between the Peierls state and an insulating state with a constant modulation wave-vector equal to the sum of the Fermi wave-vectors of the two bands. The structural phase transitions in the inorganic quasi-one-dimensional conductors are discussed and shown to be more likely to be described by a model with a phonon-mediated interaction between the two bands (g3 not=0).

Phase diagrams of systems exhibiting incommensurate structures.

The global phase diagram of a simple model exhibiting disorder-incommensurate (D-I) transition is analyzed using mean-field approximation. This phase diagram is expected to be qualitatively correct in d=3 dimensions. It is shown that depending on the parameters of this model, the D-I transition either (a) is associated with a small order parameter and may thus be described by a Landau-Ginzburg-Wilson model, or (b) has no small order parameter, and the transition takes place via condensation of solitons. The two segments of the transition line are connected by a line of first-order transitions. Applications to intercalate systems and to magnetic spirals are considered.

Magnetic phase diagram of MnAs

A Landau-type phenomenological model, involving the coupling of the first-order magnetoelastic phase transition to the second-order structural phase transition in the presence of an external magnetic field, was applied to calculate the MnAs magnetic phase diagram. The phase boundary separating the hexagonal B8 1 phase from the orthorhombic B31 phase consists of a first-order transition line and a second-order one. The main model results are: the existence of a tricritical point at the intersection of these two lines and two different regimes at the first-order phase transition line. Various experimental data for MnAs are discussed in relation to the model assumptions and results.

Phase diagrams and critical behavior of Ising square lattices with nearest-, next-nearest-, and third-nearest-neighbor couplings.

Monte Carlo simulations are used to study the location and nature of phase boundaries for Ising square lattices with antiferromagnetic coupling ${J}_{\mathrm{NN}}$ between nearest neighbors and additional interactions ${J}_{\mathrm{NNN}}$ between next-nearest neighbors and ${J}_{3\mathrm{N}\mathrm{N}}$ between third-nearest neighbors. Results in zero magnetic field are obtained for a wide range of R=${J}_{\mathrm{NNN}/{J}_{\mathrm{NN}}}$ and R'=${J}_{3\mathrm{N}\mathrm{N}/{J}_{\mathrm{NN}}}$. In addition to the c(2\ifmmode\times\else\texttimes\fi{}2) and (2\ifmmode\times\else\texttimes\fi{}1) phases, which also occur for R'=0, we find new (4\ifmmode\times\else\texttimes\fi{}4) and (4\ifmmode\times\else\texttimes\fi{}2) ordered states, for R'\ensuremath{\ne}0, which are separated from the disordered state by lines of first-order transitions. The nonuniversal critical behavior of the (2\ifmmode\times\else\texttimes\fi{}1) phase is studied using the block-distribution method and finite-size scaling. The possible existence of incommensurate phases is also explored.