Phase transitions in low-dimensional ψ 4 systems

The phase transition in a planar array of weakly coupled Ginzburg–Landau chains with real order parameter is studied, using an original variant of the two-level approximation. The results are extended to the quantum phase transition in a chain of quantum double well oscillators, coupled with an elastic interaction, using the matrix transfer method.     

The ϕ 2 4 quantum field as a limit of Sine-Gordon fields

We exhibit the λ? ₂ ⁴ quantum field theory as the limit of Sine-Gordon fields as suggested by the identity $$\varphi ^4 /4! = \mathop {\lim }\limits_{\varepsilon \to 0} (\varepsilon ^{ - 4} \cos \varepsilon \varphi - \varepsilon ^{ - 4} + \tfrac{1}{2}\varepsilon ^{ - 2} \varphi ^2 ).$$ The proofs of finite volume stability for the two models, due to Nelson and Fröhlich respectively, are unrelated. We find a generalized stability argument that incorporates ideas from both of the simpler cases. The above limit, for the Schwinger functions, then proceeds uniformly in ?. As a by-product, let (?,dμ) be a Gaussian random field, ? _K (1≦κ<∞) a regularization of ?, andV a function satisfying:

1. V(? _K )≧?ak ^α
2. ∥V(?) ?V(? _K )∥ _p≦bp ^β k ^?γ, 2≦p < ∞

Thene ^?V(?)∈L ¹(dμ) provided α(β?1)<γ.     

Phase transitions in HfV2HxD4−x: Isotope effects

The order-disorder phase transitions in HfV₂H_xD_4−x (x = 0, 1.5, 3 and 4) are studied by X-ray diffraction and NMR. In the mixed-isotope compounds two phase transitions at T₀₁ ⋍ 290 K and T₀₂ ⋍ 260 K are observed, T₀₁ and T₀₂ being close to the ordering temperatures in HfV₂H₄ and HfV₂D₄, respectively. We suggest a qualitative explanation of the isotope effect in the ordering temperature based on a model of two-sublattice interstitial site occupation with intersite “blocking”.     

The Lipatov argument for φ 3 4 perturbation theory

We extend to ₃ ⁴ the work of S. Breen on the leading behavior at large order of ₂ ⁴ perturbation theory. Using a phase space expansion to obtain new estimates on the high energy behavior of ₃ ⁴ Feynman graphs, and a rigorous semiclassical expansion, we prove that the radius of convergence of the Borel transform of the pertubative series for ₃ ⁴ Euclidean field theory is the one computed by the Lipatov method.     

Are quantum fields cellular automata?

Tesselation of the quantum field and local connectivity of the cellular automaton type is investigated. A connection between this class of models and lattice field theory is established. Nonlocal models are briefly discussed.     

Phase transitions in CuS–Ag2S nanoparticle system

(Ag₂)_xCu_1?xS, x = .2, .4, .6 and .8 nanoparticles were synthesized by the solvothermal method. The as-synthesized nanoparticles were characterized by X-ray diffraction to study the crystal structure and size. The surface morphologies of the above samples were studied using scanning electron microscope. As there is continuous shift in the lower wavelength absorption edge of the UV–VIS spectrum of these samples with concentration, (Ag₂)_xCu_1?xS nanoparticles can be tuned to different band gap energies by varying the composition. The D.C. electrical resistance was measured in the temperature range 310–485 K. As Ag₂S transforms from monoclinic to bcc at around 450 K, copper sulfide nanoparticles also shows a phase transition at around 470 K, the effects of these two transitions are seen in the resistance measurements and in the UV–VIS spectra of the entire system. The electrical resistance of (Ag₂)_xCu_1?xS nanoparticles rapidly reduces as more and more copper sulfide is added.     

A possible constructive approach to φ 4 4

We propose a constructive approach to ₄ ⁴ . It is based on formulating the ₄ ⁴ theory as an implicit function problem using multiplicative renormalization. For the corresponding lattice formulation we reduce the problem to verifying three conjectures. One conjecture is a regularity condition. The remaining two concern properties of the classical Ising ferromagnet, one of which we discuss in the frame work of critical point analysis.     

Phase transitions in the (Cs1−x Rbx)2ZnI4 system

(Cs_1−x Rb_x)₂ZnI₄ crystals were grown by two different methods with Rb concentrations varying from x=0 to 2.5%. ¹²⁷I NQR and calorimetric measurements showed that crystals grown by the Bridgman technique contain residual impurities (∼0.5%) for all x. While x=0 crystals grown from solution do not contain detectable impurities, they allow incorporation only of a low Rb concentration, not above 0.5%. A transition-temperature-concentration (x) phase diagram has been constructed for Bridgman-grown crystals from NQR data. Rb doping shifts the normal-incommensurate and incommensurate-ferroelastic phase-transition points toward higher temperatures with different rates. The P2₁/m↔P1 first-order transition shifts toward lower temperatures. The region of low Rb concentrations lies closest to the critical point. Fiz. Tverd. Tela (St. Petersburg) 41, 143–147 (January 1999)     

Phase transitions in “small” systems

Traditionally, phase transitions are defined in the thermodynamic limit only. We discuss how phase transitions of first order (with phase separation and surface tension), continuous transitions and (multi)-critical points can be seen and classified for small systems. “Small” systems are systems where the linear dimension is of the characteristic range of the interaction between the particles; i.e. also astrophysical systems are “small” in this sense. Boltzmann defines the entropy as the logarithm of the area of the surface in the mechanical N-body phase space at total energy E. The topology of S(E,N) or more precisely, of the curvature determinant allows the classification of phase transitions without taking the thermodynamic limit. Micro-canonical thermo-statistics and phase transitions will be discussed here for a system coupled by short range forces in another situation where entropy is not extensive. The first calculation of the entire entropy surface S(E,N) for the diluted Potts model (ordinary (q=3)-Potts model plus vacancies) on a square lattice is shown. The regions in {E,N} where D>0 correspond to pure phases, ordered resp. disordered, and D<0 represent transitions of first order with phase separation and “surface tension”. These regions are bordered by a line with D=0. A line of continuous transitions starts at the critical point of the ordinary (q=3)-Potts model and runs down to a branching point P_m. Along this line vanishes in the direction of the eigenvector of D with the largest eigen-value . It characterizes a maximum of the largest eigenvalue . This corresponds to a critical line where the transition is continuous and the surface tension disappears. Here the neighboring phases are indistinguishable. The region where two or more lines with D=0 cross is the region of the (multi)-critical point. The micro-canonical ensemble allows to put these phenomena entirely on the level of mechanics. Received 18 October 1999 and received in final form 17 November 1999     

The critical behavior of φ 1 4

The eigenvalues, eigenfunctions, and Schwinger functions of the ordinary differential operator $$H(\lambda ,m) = \tfrac{1}{2}\{ p^2 + \lambda q^4 + (m^2 - \lambda m^{ - 2} )q^2 \} $$ are studied as λ → ∞. It is shown that the scaling limit of the Schwinger functions equals the scaling limit of a one dimensional Ising model. Critical exponents ofH(λ,m) are shown to equal critical exponents of the Ising model, while critical exponents of the renormalized theory are shown to agree with those of a harmonic oscillator.     

Perturbative renormalization of massless φ 4 4 with flow equations

Perturbative renormalizability proofs in the Wilson-Polchinski renormalization group framework, based on flow equations, were so far restricted to massive theories. Here we extend them to Euclidean massless φ ₄ ⁴ . As a by-product of the proof we obtain bounds on the singularity of the Green functions at exceptional momenta in terms of the exceptionality of the latter. These bounds seem to be new and are quite sharp.     

Phase transitions in h-thiourea under electric‐field

Abstract

Dielectric constant, spontaneous polarization and pyroelectric response measurements were performed on thin samples (e < 100 μm) of H-thiourea as a function of temperature and applied electric field. Along with previous data obtained by optical birefringence, X-ray and neutron diffraction techniques, the results put in evidence three features in the modulated region between the ferroelectric state and the paraelectric one. The tricritical point is determined for E_tr ? 2075 V/mm and T_tr ? 192 K.     

Phase transitions in a hydrogen-rich compound：tetramethylsilane

High-pressure behavior of tetramethylsilane is investigated by synchrotron powder X-ray diffraction and Raman scattering at pressures up to 30 GPa and room temperature. Our results reveal the analogous phase transitions, though slight hysteresis for the certain phases. A new phase is found to appear at 4.2 GPa due to the disappeared Raman mode. These findings offer the possibility to understand the evolution of the H-H bonding with pressure in such hydrogen-rich compounds.     

Phase transitions for an ideal Bose condensate trapped in?a?quartic potential

Based on the classification scheme of phase transitions, we study the phase transitions for an ideal Bose gas with a finite number of particles confined in a three-dimensional quartic trap. We show that the phase transition of an ideal Bose gas in the three-dimensional quartic trap is of third order for finite particle numbers, quite different from the fact that the phase transition is of first order in the thermodynamic limit. We discuss the effects of finite particle numbers on the nature of the phase transitions, and determine the dependence of transition temperature on particle number.     

Calculation of the Specific Heats for the Ⅱ—Ⅲ and Ⅱ—Ⅳ Phase transitions in NH4I

This study gives our calculation for the specific heats CVI due to an Ising model using the observed Cp data for the Ⅱ-Ⅲ and Ⅱ-VI phase transitions in NH4I.By fitting to the CP data we determine the values of the critical exponent for the pressure of 0.14GPa(Ⅱ-Ⅲ phase transition)and for the pressures of 0.75,1.35and 1.97 GPa (II-IV phase transition)in NH4I.Our exponent values values are close to the predicted values of the specific heat in a three-dimensional Ising model.Our calculated CVI are in good agreement with the experimental CP for NH4I in most cases.     

Block spin approach to φ 3 4 field theory

A block spin approach to the Euclidean ⁴ field theory in three dimensions is proposed by using the three-dimensional version of Gawedzki and Kupiainen's block spin transformation method. The lattice ₃ ⁴ model recovers the rotation invariance in the continuum limit, when the coupling constant is small.     

Magnetic transitions in K2MnCl4·2H2O

Results of (dM/dH) measurements on tetrahedral K₂MnCl₄·2H₂O as a function of temperature and magnetic field, are presented. An antiferromagnetic transition along the tetragonal axis is observed at T_N = (3.05±0.05) K. The H-T magnetic phase diagram was completely determined, and shows the usual characteristics of that of a low anisotropy antiferromagnet. The T = 0 critical fields are compatible with the values H_E = (29.2±0.3) kOe and H_A = (5.9±0.6) kOe for the exchange and anisotropy fields.     

Local existence of the Borel transform in Euclidean φ 4 4

We bound rigorously the large order behaviour of ₄ ⁴ euclidean perturbative quantum field theory, as the simplest example of renormalizable, but non-super-renormalizable theory. The needed methods are developed to take into account the structure of renormalization, which plays a crucial role in the estimates. As a main thorem, it is shown that the Schwinger functions at ordern are bounded byK ⁿ n!, which implies a finite radius of convergence for the Borel transform of the perturbation series.