Coupled m-component fields with cubic anisotropy

The critical behavior at phase transitions of two coupled, m-component systems with cubic anisotropy is studied by a simplified model in which the fluctuations are partially considered. The phase transition could be a new fluctuation-induced first order transition into the anisotropic phase, or a new second order phase transition. Unlike in uncoupled systems, the second order phase transition could be into either the anisotropic or isotropic phase. As expected, upon suppression of fluctuations, all results reduce to those of mean field theory.     

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.     

The Mössbauer effect and magnetic phase transitions

The Mössbauer effect provides a direct method for identifying the spin axis in magnetic crystals and observing magnetic phase transitions. The order of the transition may be inferred from the Mössbauer spectrum. Phase changes can occur as a function of temperature (e.g. when the anisotropy fieldB _A changes sign) or as a function of applied magnetic field. In an antiferromagnet a field ?(2B _E B _A)^1/2 along the spin axis whereB _E is the exchange field causes the spin-flop transition which is normally first order (sharp) whereas the transition to the paramagnetic phase which occurs at higher fields?2B _E is second order (continuous). In quasi-one-dimensional crystals Mössbauer spectra show that the spin-flop transition is first order locally but occurs over a range of fields throughout the crystal, so that the first order character is masked in a conventional magnetization measurement. In fields applied at a finite angle>B _A/2B _E to the spin axis the transition becomes second order, i.e. a continuous rotation of the spins occurs. In canted antiferromagnets (or weak ferromagnets) the spin-flop transition is also continuous; in addition a “screw” re-orientation may be induced by fields applied perpendicular to the spin axis and arises from antisymmetric exchange. For crystals with lowT _N the hyperfine field changes when a magnetic field is applied and has a minimum at a phase transition; this may be used to map out the magnetic phase diagram.     

Change in the order of a martensitic phase transformation by an external field

It is shown on the basis of the Labbé-Friedel model for A₃B compounds that the martensitic phase transformation in Nb₃Sn can be changed from a first to a second order transition by an external stress. The Hamiltonian operator describing the phase transition in an external stress field has been mapped to a spin $\text{1}\text{2}$ Ising model with infinite range interactions showing a second order phase transition. Estimates of the transition temperature and the maximum order parameter are given suggesting new experiments.     

Precursor state of skyrmions in MnSi: a heat capacity study

The magnetic phase diagram of MnSi based on the detailed magneto‐heat capacity study is presented. It shows the A‐phase, a precursor to the formation of stable skyrmion lattice, along with the intermediate, helical, conical, ferromagnetic and paramagnetic phases. The field isotherms of specific heat in and around the transition temperature reveal the different magnetic modulations. The local minima represent the relatively low entropy state due to the formation of A‐phase as a precursor to the stable skyrmion lattice. The field‐induced second‐order phase transition is observed by melting the intermediate phase. The region of existence of first‐order phase transition is found to be, effectively, from helical to the intermediate phase. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Random crystal-field effects in a mixed spin-1/2 and spin-2 ferrimagnetic Ising system

The magnetic properties of a mixed spin ferrimagnetic system σ?=?1/2 and S?=?2 at the sites of a square lattice with a random crystal field are studied by the mean field approximation. The ground state of the system is determined and the total magnetization is plotted according to the model parameters. Different behaviors for the thermal dependence of the magnetization are highlighted. In particular, one sees the appearance of one or two compensating points and many types of phase diagrams with first and second order phase transition lines as well as isolated critical and tricritical points.     

The field induced magnetization reorientation in weak ferromagnets—III: The case of non-equivalent single ion anisotropy

The phase transitions in a single-ion anisotropy type weak ferromagnet at 0°K are studied using a two sublattice model and molecular field theory. In an external field applied along the antiferromagnetic axis, there exist three stable phases, denoted as weak ferromagnetic (WF), spin-flop (SF), and metamagnetic (MM). The character of the WF to SF transition changes from first to second order as the angle between a sublattice uniaxial anisotropy axis and the antiferromagnetic axis is increased. The tricritical field for this phase transition is proportional to the one-half power of the uniaxial anisotropy field, when the latter is much smaller than the exchange field. The transitions to and from the MM phase are always of first order. The former can result from either a WF or a SF phase instability threshold being reached. The latter always results in a transition to the WF phase. All three phases can, under specified conditions, coexist for a range of applied field values. In this case, an instability of the WF phase always results in a first order transition to the SF phase.     

Percolation Phase Transitions from Second Order to First Order in Random Networks

We investigate a percolation process where an additional parameter q is used to interpolate between the classical Erd¨os–R′enyi(ER) network model and the smallest cluster(SC) model. This model becomes the ER network at q = 1, which is characterized by a robust second order phase transition. When q = 0, this model recovers to the SC model which exhibits a first order phase transition. To study how the percolation phase transition changes from second order to first order with the decrease of the value of q from 1 to 0, the numerical simulations study the final vanishing moment of the each existing cluster except the N-cluster in the percolation process. For the continuous phase transition,it is shown that the tail of the graph of the final vanishing moment has the characteristic of the convexity. While for the discontinuous phase transition, the graph of the final vanishing moment possesses the characteristic of the concavity.Just before the critical point, it is found that the ratio between the maximum of the sequential vanishing clusters sizes and the network size N can be used to decide the phase transition type. We show that when the ratio is larger than or equal to zero in the thermodynamic limit, the percolation phase transition is first or second order respectively. For our model, the numerical simulations indicate that there exists a tricritical point qcwhich is estimated to be between0.2 qc 0.25 separating the two phase transition types.     

Microcanonical Analysis on a System with Long-Range Interactions

We study a long-range interacting spin chain placed in a staggered magnetic field using microcanonical approach and obtain the global phase diagram. We find that this model exhibits both first order phase transition and second order phase transition separated by a tricritical point, and temperature jump can be observed in the first order phase transition.     

Gelation as a rod-glass transition

A sol-gel transition of rod-like macromolecules in solution is viewed as a rod-glass transition, similar to the spin-glass transition in dilute magnetic systems. A molecular field theory for the order parameters is presented. Varying the disorder parameter an ordered nematic-like phase is found for zero disorder, exhibiting first order transition, while a rod-glass second order transition is found for maximal disorder. A remanent nematic-like order always accompanies the glass phase, unlike the case of magnetic spin-glass.     

New superconducting phases in field-induced organic superconductor lambda-(BETS)2FeCl4

We derive the parallel upper critical field, Hc2, as a function of the temperature T in quasi-2D organic compound lambda-(BETS)2FeCl4, accounting for the formation of the nonuniform Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state. To further check the 2D LOFF model, we propose to study the Hc2(T) curve at low T in tilted fields, where the vortex state is described by the high Landau level functions characterized by the index n. We predict a cascade of first-order transitions between vortex phases with different n, between phases with different types of the symmetry at given n and the change of the superconducting transition from the second order to the first order as FeCl4 ions are replaced partly by GaCl4 ions.     

The large polaron in a magnetic field: Possible existence of a phase transition

It is shown that the ground state energy of a polaron in a magnetic field (calculated in the Feynman approximation) exhibits a discontinuity in the first derivative with respect to α (the electron-phonon coupling constant) if ω_c/ω_o (cyclotron frequency to LO-phonon frequency) is larger than 2.24. This discontinuity has the characteristics of a first order phase transition if α is interpreted as an inverse temperature. For ω_c/ω_o = 2.24 the transition is second order. We found that below the transition point the phonon cloud cannot follow the electron in its motion in the magnetic field.     

First and second order transition in frustrated XY systems

The nature of the phase transition for the XY stacked triangular antiferromagnet (STA) is a controversial subject at present. The field theoretical renormalization group (RG) in three dimensions predicts a first order transition. This prediction disagrees with Monte-Carlo (MC) simulations which favor a new universality class or a tricritical transition. We simulate by the Monte-Carlo method two models derived from the STA by imposing the constraint of local rigidity which should have the same critical behavior as the original model. A strong first order transition is found. Following Zumbach we analyze the second order transition observed in MC studies as due to a fixed point in the complex plane. We review the experimental results in order to clarify the critical behavior observed. Received: 18 February 1998 / Revised: 24 April 1998 / Accepted: 30 April 1998     

在高密度下核物质的色超导性

建立了相变热力学理论和场论的关系. 强调在量子场论中必须引进序参量场， 则相变的讨论就类似于Goldstone bosons 的产生. 如果只讨论一级相变， Goldstone bosons场就足够了; 如果要讨论二级相变， 则必须讨论一系列的场， 这些场构成一个对称群的表示. 另外, 也将这一思想用到色超导中. In this paper we built a relation between the thermodynamical theory of the phase transition and field theory. We emphasized that in the quantum field theory we have to introduce the order parameter fields. Then the discussion of the phase transition is closed to the creation of the Goldstone bosons. If we only discuss the first order transition, the Goldstone bosons fields are sufficient. If we want to discuss the second order transition, we have to discuss a set of fields that constructs a representation of a symmetry group. We also apply this concept to color superconductivity.     

Singular renormalization group transformations and first order phase transitions (II). Monte Carlo renormalization group results

The first order phase transitions in the two-dimensional 10-state Potts model and in the two-dimensional Ising model with magnetic field are studied with Monte Carlo renormalization group methods. The deconfining phase transition of the four-dimensional U(1) lattice gauge theory is treated similarly. The results are not consistent with the standard discontinuity fixed point picture of first order phase transitions. In the U(1) case, where this possibility exists, they are not consistent with a second order phase transition either. The results show a discontinuous flow on the first order transition surface, which is a Monte Carlo renormalization group signal of singular RG transformations.     

Photon,quantum and collective,effects from rydberg atoms in cavities

I review some theories of the interaction ofN Rydberg atoms interacting collectively with radiation in microwave cavities. The radiation may be incoherent (black body) radiation or it may be coherent. In the former case theories of the steady state inversion and of the superradiance from initially inverted atoms in low-Q cavities agree well with experimental observations. In the latter case in low-Q cavities ‘phase transitions’ of both first and second order types are predicted and should be observable by monitoring the output of an atomic beam by an atomic ionisation detector. The first order transition which occurs at opposite detunings of the cavity and atoms from the frequency of the coherent driving field is of “optically” bistable type but hysteresis is suppressed by quantum fluctuations which can be large in the cavity field close to the transition. I also review a theory of the spectra from single atoms in cavities ofarbitrary Q containing a few microwave photons. A transition from a single peaked Lorentzian spectrum at low-Q to a double-peaked spectrum forQ≃10⁶ is predicted and peaks representing one or more photon transitions of the Jaynes-Cummings model are also expected to be observable at these or largerQ values. The collective theories are all based onN atom Dicke type models driven by the coherent or incoherent field. Substantial squeezing of the fluorescent radiation field from these Dicke models is also predicted and may be observable with Rydberg atoms.     

Hybrid Weyl semimetal under crossed electric and magnetic fields: Field tuning of spectrum type

There are two types (WSM-I and WSM-II) of the WSMs. The WSMs of different types have various topological and transport properties. Besides pure WSM-I and WSM-II, there exists a novel type, dubbed “hybrid Weyl semimetal”, which contains the Weyl points of both types. In this Letter we consider the hybrid WSM under crossed magnetic and electric fields. The electromagnetic field induces transition between different types of spectrum in Weyl point (WP). Thus, hybrid phase of the WSM can be tunable using the electromagnetic field. Finally, we proposed a new field-induced type of hybrid WSM in which two different regimes of spectrum coexist. In this case, the spectrum near the first WP corresponds to electric regime (no Landau levels) and the spectrum in the second WP with opposite chirality corresponds to magnetic regime (there are Landau levels).     

A μSR-study of UP and UTe

The materials crystallize in the NaCl structure. UP undergoes at 122 K a first order transition into a type I single-k antiferromagnetic state, followed by a second first order transition into a type I double-k-structure at 22 K. UTe is a ferromagnet withT _c =104 K. The two first order transitions of UP reveal themselves by abrupt changes of the transverse field damping rate. No spin rotation is observed in zero field for both antiferromagnetic spin structures which is in keeping with point dipolar lattice sums. In UTe we observe the characteristic critical behavior: a rapid increase of damping rate and paramagnetic frequency shift when approachingT _c from above. In the ferromagnetic regime the spin rotation in zero field damps out too rapidly to be observed. This work has been funded in part by the German Federal Minister for Research and Technology (BMFT) under contract Nr. 03-KA1-TUM-4.     

Mean field approach to finite temperature gauge systems

We apply a mean field treatment to theZ ₂ andZ ₃ gauge systems at finite temperature. In the lowest order the deconfinement of fixed electric charges is a second order transition forZ ₂ and a first order transition forZ ₃. Higher order corrections can be calculated using the steepest descent method.     

Fulde-Ferrell-Larkin-Ovchinnikov state in layered superconductors

The phase diagram of a layered superconductor in a large parallel magnetic field is calculated. This includes a calculation of the lower critical field beyond which the superconductor is in the FFLO-state and possesses a spatially modulated order parameter and spin polarization. The order parameter, spin polarization, free-energy density, and phase boundaries of this unconventional superconducting phase are evaluated numerically in the complete B–T plane. The analysis suggests that the transition at the lower critical field is of second order, and not of first order, as previously assumed. The order parameter of the FFLO-state merges continuously into the uniform superconducting state.