Low-temperature Series Research Articles

On general-n coefficients in series expansions for row spin–spin correlation functions in the two-dimensional Ising model

We consider spin–spin correlation functions for spins along a row, R n = ⟨σ 0,0 σ n,0⟩, in the two-dimensional Ising model. We discuss a method for calculating general-n expressions for coefficients in high-temperature and low-temperature series expansions of R n and apply it to obtain such expressions for several higher-order coefficients. In addition to their intrinsic interest, these results could be useful in the continuing quest for a nonlinear ordinary differential equation whose solution would determine R n , analogous to the known nonlinear ordinary differential equation whose solution determines the diagonal correlation function ⟨σ 0,0 σ n,n ⟩ in this model.

FABRICATION AND CHARACTERIZATION OF LTCC BASED ON TALK GLASSES

In this work, fabrication of low temperature co-fired (LTCC) with different Talc content is performed. Density and mechanical characterization of the prepared samples has been examined. Three series of low temperature co-fired ceramics have been prepared. The glass part of these composites contains talc to enhance the mechanical properties. The densities, hardness and splitting strength are measured for these series to monitor the effect of composition on their properties. It is shown that the third series (Base3; Flint 25%, talc 35%, Pota ash 8%, Soda ash 12%, and Boric Acid 20%) of the higher talc content shoes the better densities and mechanical properties. The results are explained in terms of better balance of the ceramic-class content that enhances the measured properties.

Spin order and entropy in antiferromagnetic films subjected to magnetic fields

Using systematic effective field theory, we explore the properties of antiferromagnetic films subjected to magnetic and staggered fields that are either mutually aligned or mutually orthogonal. We provide low-temperature series for the entropy density in either case up to two-loop order. Invoking staggered, uniform and sublattice magnetizations of the bipartite antiferromagnet, we investigate the subtle order–disorder phenomena in the spin arrangement, induced by temperature, magnetic and staggered fields—some of which are quite counterintuitive. In the figures we focus on the spin- square-lattice antiferromagnet, but our results are valid for any other bipartite two-dimensional lattice.

Kinematic interaction and condensation factor in two-dimensional quantum Heisenberg ferromagnet

We investigate the influences of Dyson’s kinematic and dynamic interaction on the physical properties of two-dimensional quantum Heisenberg ferromagnet with O(3) rotational symmetry. It is found that the repulsive potential led by dynamic interaction modifies the third large term with $$T^{3}$$ in the low-temperature series of specific heat. Under mean-field approximation, the kinematic interaction transforms the occupation-number configuration into a coherent-state configuration and significantly improves the result of modified spin wave theory in the high-temperature limit. In the low-temperature limit, the kinematic-interaction contribution to specific heat is negligibly small. For finite-size systems, it is found that a crossover temperature can be used to characterize the transition to a single-domain-type magnet. In the thermodynamic limit, the condensation factor (the number of zero-mode magnons) dominates the isothermal compressibility of magnon gas although there is not a real phase transition at finite temperatures. The asymptotic behavior of static structure factor depends on the relative size of the spin-wave wavelength with respect to the correlation length.

Uniform perpendicular and parallel staggered susceptibility of antiferromagnetic films

We investigate the thermodynamic behavior of antiferromagnetic films in external magnetic fields oriented perpendicular to the staggered magnetization. Within the systematic effective Lagrangian framework we first calculate the two-point function and the dispersion relation for the two types of magnons up to one-loop order. This allows us to split the two-loop free energy density into a piece that originates from noninteracting dressed magnons, and a second piece that corresponds to the genuine magnon–magnon interaction. We then discuss the low-temperature series for various thermodynamic quantities, including the parallel staggered and uniform perpendicular susceptibilities, and analyze the role of the spin–wave interaction at finite temperature.

Thermodynamics of antiferromagnetic solids in magnetic fields

We analyze the thermodynamic properties of antiferromagnetic solids subjected to a combination of mutually orthogonal uniform magnetic and staggered fields. Low-temperature series for the pressure, order parameter and magnetization up to two-loop order in the effective expansion are established. We evaluate the self-energy and the dispersion relation of the dressed magnons in order to discuss the impact of spin–wave interactions on thermodynamic observables.

Critical properties of the Ising model in hyperbolic space.

The Ising model exhibits qualitatively different properties in hyperbolic space in comparison to its flat space counterpart. Due to the negative curvature, a finite fraction of the total number of spins reside at the boundary of a volume in hyperbolic space. As a result, boundary conditions play an important role even when taking the thermodynamic limit. We investigate the bulk thermodynamic properties of the Ising model in two- and three-dimensional hyperbolic spaces using Monte Carlo and high- and low-temperature series expansion techniques. To extract the true bulk properties of the model in the Monte Carlo computations, we consider the Ising model in hyperbolic space with periodic boundary conditions. We compute the critical exponents and critical temperatures for different tilings of the hyperbolic plane and show that the results are of mean-field nature. We compare our results to the "asymptotic" limit of tilings of the hyperbolic plane: the Bethe lattice, explaining the relationship between the critical properties of the Ising model on Bethe and hyperbolic lattices. Finally, we analyze the Ising model on three-dimensional hyperbolic space using Monte Carlo and high-temperature series expansion. In contrast to recent field theory calculations, which predict a non-mean-field fixed point for the ferromagnetic-paramagnetic phase-transition of the Ising model on three-dimensional hyperbolic space, our computations reveal a mean-field behavior.

The bulk, surface and corner free energies of the anisotropic triangular Ising model

We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman’s spinor method to calculate low-temperature series expansions for the partition function to high order. From these, we can obtain 108-term series expansions for the bulk, surface and corner free energies. We extrapolate these to all terms and thereby conjecture the exact results for each. Our results agree with the exactly known bulk-free energy and with Cardy and Peschel’s conformal invariance predictions for the dominant behaviour at criticality. For the isotropic case, they also agree with Vernier and Jacobsen’s conjecture for the 60 ° corners.

Duality and free energy analyticity bounds for few-body Ising models with extensive homology rank

We consider pairs of few-body Ising models where each spin enters a bounded number of interaction terms (bonds) such that each model can be obtained from the dual of the other after freezing k spins on large-degree sites. Such a pair of Ising models can be interpreted as a two-chain complex with k being the rank of the first homology group. Our focus is on the case where k is extensive, that is, scales linearly with the number of bonds n. Flipping any of these additional spins introduces a homologically nontrivial defect (generalized domain wall). In the presence of bond disorder, we prove the existence of a low-temperature weak-disorder region where additional summation over the defects has no effect on the free energy density f(T) in the thermodynamical limit and of a high-temperature region where an extensive homological defect does not affect f(T). We also discuss the convergence of the high- and low-temperature series for the free energy density, prove the analyticity of limiting f(T) at high and low temperatures, and construct inequalities for the critical point(s) where analyticity is lost. As an application, we prove multiplicity of the conventionally defined critical points for Ising models on all { f, d} tilings of the infinite hyperbolic plane, where df/(d + f) > 2. Namely, for these infinite graphs, we show that critical temperatures with free and wired boundary conditions differ, Tc(f)<Tc(w).

Supersymmetric t-J models with long-range interactions: thermodynamics and criticality

We analyze the thermodynamics and the critical behavior of the supersymmetric t-J model with long-range interactions. Using the transfer matrix formalism, we obtain a closed-form expression for the free energy per site both for a finite number of sites and in the thermodynamic limit. Our approach, which is different from the usual ones based on the asymptotic Bethe ansatz and generalized exclusion statistics, can in fact be applied to a large class of models whose spectrum is described in terms of supersymmetric Young tableaux and their associated Haldane motifs. In the simplest and most interesting case, we identify the five ground state phases of the model and derive the complete low-temperature asymptotic series of the free energy per site, the magnetization and charge densities, and their susceptibilities. We verify the model’s characteristic spin-charge separation at low temperatures, and show that it holds to all orders in the asymptotic expansion. Using the low-temperature asymptotic expansions of the free energy, we also analyze the critical behavior of the model in each of its ground state phases. While the standard phase is described by two independent conformal field theories (CFTs) with central charge c = 1 in correspondence with the spin and charge sectors, we find that the low-energy behavior of the and phases is that of a single c = 1 CFT. We show that the model exhibits an even richer behavior on the boundary between zero-temperature phases, where it can be non-critical but gapless, critical in the spin sector but not in the charge one, or critical with central charge c = 3/2.

Spin-wave thermodynamics of square-lattice antiferromagnets revisited

Modifying the conventional spin-wave theory in a novel manner based on the Wick decomposition, we present an elaborate thermodynamics of square-lattice quantum antiferromagnets. Our scheme is no longer accompanied by the notorious problem of an artificial transition to the paramagnetic state inherent in modified spin waves in the Hartree-Fock approximation. In the cases of spin $\frac{1}{2}$ and spin $1$, various modified-spin-wave findings for the internal energy, specific heat, static uniform susceptibility, and dynamic structure factor are not only numerically compared with quantum Monte Carlo calculations and Lanczos exact diagonalizations but also analytically expanded into low-temperature series. Modified spin waves interacting via the Wick decomposition provide reliable thermodynamics over the whole temperature range of absolute zero to infinity. Adding higher-order spin couplings such as ring exchange interaction to the naivest Heisenberg Hamiltonian, we precisely reproduce inelastic-neutron-scattering measurements of the high-temperature-superconductor-parent antiferromagnet $\mathrm{La}_2\mathrm{CuO}_4$. Modifying Dyson-Maleev bosons combined with auxiliary pseudofermions also yields thermodynamics of square-lattice antiferromagnets free from thermal breakdown, but it is less precise unless temperature is sufficiently low. Applying all the schemes to layered antiferromagnets as well, we discuss the advantages and disadvantages of modified spin-wave and combined boson-pseudofermion representations.

Synthesis of Predesigned Ferroelectric Liquid Crystals and Their Applications in Field‐Sequential Color Displays

AbstractA series of low transition temperature and fast response chiral smectic C (SmC*) liquid crystals is designed and synthesized. The phase transition behaviors and electrooptical properties of the synthesized compounds are investigated and compared with reported values. The ferroelectric phase of the liquid crystals is characterized by means of differential scanning calorimetry, polarizing optical microscopy, wide‐angle X‐ray scattering (WAXS), and electrooptical measurements. The wide SmC* phase is achieved via the induction of achiral trisiloxane and a chiral methyl‐lateral substituent onto the terminuses of the molecules. The optimized packing arrangement model is studied based on the exceptionally high apparent tilt angles (≈41°) and smectic layer spacing observed using WAXS. A fast response time of 0.3 ms in an electric field of 10 V µm−1 provides an opportunity to use the synthesized materials for field‐sequential color liquid crystal displays (FSCLCDs). An FSCLCD sample cell is fabricated using the synthesized ferroelectric liquid crystals via a red (R), green (G), and blue (B) backlight. A color‐frame frequency of more than 500 Hz (i.e., a frame frequency more than 166 Hz) is achieved. As a single material liquid crystal display cell, the synthesized ferroelectric liquid crystals show great performances at room temperature.

Investigating on sintering mechanism and adjustable dielectric properties of BLMT glass/Li2Zn3Ti4O12 composites for LTCC applications

A series of novel low temperature co-fired ceramics were fabricated in x BLMT-(100-x) Li2Zn3Ti4O12 (2.5 ≤ x ≤ 80 wt%) composites sintered at 900 °C. The sintering mechanism, phase composition, microstructure and dielectric properties of the composites were investigated. The results showed that the sintering mechanism of composites with <20 wt% BLMT glass could be attributed to non-reactive liquid-phase sintering and LaBO3 phase was crystallized from glass beside Li2Zn3Ti4O12 phase, while composites with ≥20 wt% glass were controlled by the coexistence of viscous sintering and reactive liquid-phase sintering, BLMT glass crystallized forming LaBO3, MgLaB5O10 and a small amount of rutile phase, nevertheless, more rutile phase was formed by reacting between glass and ceramic. As BLMT glass was increased, LaBO3, MgLaB5O10 and rutile phase gradually dominated the material and Li2Zn3Ti4O12 phase decreased. Meanwhile, the dielectric constant (εr) and quality factor (Q × f) demonstrated gradually decrease, whereas the temperature coefficient of resonant frequency (τf) presented a trend of fall first then rise. Typically, the composite with 60 wt% glass displayed excellent dielectric properties with εr = 14, Q × f = 23,000 GHz, and τf = −3.56 ppm/°C. The corresponding fitting equations of εr, Q × f and τf on the BLMT glass content were obtained by the Origin software, which indicated that the dielectric properties of BLMT/Li2Zn3Ti4O12 composites could be precisely adjusted by adding the suitable content of glass. Therefore, the sintering process, phase composition and dielectric properties of BLMT/Li2Zn3Ti4O12 composites can be controlled by varying the content of Li2Zn3Ti4O12 ceramic and B2O3-La2O3-MgO-TiO2 glass.

Repeated freezing induces a trade-off between cryoprotection and egg production in the goldenrod gall fly, Eurosta solidaginis.

Internal ice formation leads to wholesale changes in ionic, osmotic and pH homeostasis, energy metabolism, and mechanical damage, across a small range of temperatures, and is thus an abiotic stressor that acts at a distinct, physiologically relevant, threshold. Insects that experience repeated freeze-thaw cycles over winter will cross this stressor threshold many times over their lifespan. Here, we examined the effect of repeatedly crossing the freezing threshold on short-term physiological parameters (metabolic reserves and cryoprotectant concentration) as well as long-term fitness-related performance (survival and egg production) in the freeze-tolerant goldenrod gall fly, Eurosta solidaginis We exposed overwintering prepupae to a series of low temperatures (-10, -15 or -20°C) with increasing numbers of freezing events (3, 6 or 10) with differing recovery periods between events (1, 5 or 10 days). Repeated freezing increased sorbitol concentration by about 50% relative to a single freezing episode, and prompted prepupae to modify long-chain triacylglycerols to acetylated triacylglycerols. Long-term, repeated freezing did not significantly reduce survival but did reduce egg production by 9.8% relative to a single freezing event. Exposure temperature did not affect any of these measures, suggesting that threshold crossing events may be more important to fitness than the intensity of stress in overwintering E. solidaginis.

Antiferromagnetic films in weak magnetic and staggered fields

We study the low-temperature behavior of antiferromagnets in two spatial dimensions that are subjected to a magnetic field oriented perpendicular to the staggered magnetization order parameter. The evaluation of the partition function is carried to two-loop order within the systematic effective Lagrangian technique. Low-temperature series that are valid in weak magnetic and staggered fields are derived for the pressure, staggered magnetization, and magnetization. Remarkably, at $T$=0, the staggered magnetization is enhanced by the magnetic field, implying that the phenomenon of magnetic catalysis also emerges in antiferromagnetic films.

Exchange-coupled terbium-radical complex Tb-phNO showing slow reversal of magnetization

A novel terbium(III)-nitroxide complex [TbIII(hfac)3(phNO)(H2O)] (phNO=tert-butyl phenyl nitroxide, hfac=1,1,1,5,5,5-hexafluoropentane-2,4-dionate) was synthesized towards development of 4f-2p compounds with strong ferromagnetic exchange coupling. There are two crystallographically independent molecules in a unit cell. The ac magnetic susceptibility at Hdc=2000Oe showed double χm″ peaks accompanied by frequency dependence and afforded Ueff(1)/kB=46.3(7)K with τ0(1)=1.9(3)×10−9s for the high-temperature peak series and Ueff(2)/kB=21(2)K with τ0(2)=1.3(9)×10−8s for the low-temperature peak series. Every molecule is proven to behave as a potential single-molecule magnet (SMM). In contrast, the corresponding dysprosium(III) analogue did not exhibit meaningful out-of-phase ac magnetic susceptibility. In the strongly exchange-coupled regime owing to the direct radical coordination bond, the whole molecular electron counting may provide a useful criterion to predict Kramers molecules as potential SMM candidates.

Cubic ideal ferromagnets at low temperature and weak magnetic field

The low-temperature series for the free energy density, pressure, magnetization and susceptibility of cubic ideal ferromagnets in weak external magnetic fields are discussed within the effective Lagrangian framework up to three loops. The structure of the simple, body-centered, and face-centered cubic lattice is taken into account explicitly. The expansion involves integer and half-integer powers of the temperature. The corresponding coefficients depend on the magnetic field and on low-energy effective constants that can be expressed in terms of microscopic quantities. Our formulas may also serve as efficiency or consistency check for other techniques like Green's function methods, where spurious terms in the low-temperature expansion have appeared. We explore the sign and magnitude of the spin-wave interaction in the pressure, magnetization and susceptibility, and emphasize that our effective field theory approach is fully systematic and rigorous.

Unprecedented Integral-Free Debye Temperature Formulas: Sample Applications to Heat Capacities of ZnSe and ZnTe

Detailed analytical and numerical analyses are performed for combinations of several complementary sets of measured heat capacities, for ZnSe and ZnTe, from the liquid-helium region up to 600 K. The isochoric (harmonic) parts of heat capacities, CVh(T), are described within the frame of a properly devised four-oscillator hybrid model. Additional anharmonicity-related terms are included for comprehensive numerical fittings of the isobaric heat capacities, Cp(T). The contributions of Debye and non-Debye type due to the low-energy acoustical phonon sections are represented here for the first time by unprecedented, integral-free formulas. Indications for weak electronic contributions to the cryogenic heat capacities are found for both materials. A novel analytical framework has been constructed for high-accuracy evaluations of Debye function integrals via a couple of integral-free formulas, consisting of Debye’s conventional low-temperature series expansion in combination with an unprecedented high-temperature series representation for reciprocal values of the Debye function. The zero-temperature limits of Debye temperatures have been detected from published low-temperature Cp(T) data sets to be significantly lower than previously estimated, namely, 270 (±3) K for ZnSe and 220 (±2) K for ZnTe. The high-temperature limits of the “true” (harmonic lattice) Debye temperatures are found to be 317 K for ZnSe and 262 K for ZnTe.

Effect of laser surface remelting and low temperature aging treatments on microstructures and surface properties of Ti-55511 alloy

The near-β titanium alloy Ti-5Al-5Mo-5V-1Cr-1Fe (Ti-55511) was firstly remelted on the surface by laser and a series of subsequent low temperatures aging treatments were carried out to obtain ultrafine microstructures in the remelted layer. Microhardness and wear resistance of each treated sample were then tested to evaluate the effects of ω-assisted α phase on the surface properties. Microstructure evolution of the whole process was observed by optical and electron microscopes. Results showed that nano-scaled athermal ω phase uniformly precipitated in β matrix of Ti-55511 after rapid solidification, and it had a little reinforcement effects in the remelted layer due to the low contents. After low temperatures aging, ultrafine α lamellas could form in the remelted layer by ω-assisted nucleation. By increasing the aging temperatures, the sizes and volume fractions of α lamellas increase, resulting in an improvement of surface hardness and wear resistance. However, the high surface hardness did not effectively enhance the wear resistance of Ti-55511 due to the ductility deterioration caused by nano-sized α phase of the aged samples. The remelted samples can achieve the highest surface microhardness over 520HV and relatively best wear resistance after aging at 500°C for 5h.

Is the full susceptibility of the square-lattice Ising model a differentially algebraic function?

We study the class of non-holonomic power series with integer coefficients that reduce, modulo primes, or powers of primes, to algebraic functions. In particular we try to determine whether the susceptibility of the square-lattice Ising model belongs to this class, and more broadly whether the susceptibility is a solution of a differentially algebraic equation. Initial results on Tutte's nonlinear ordinary differential equation (ODE) and other simple quadratic nonlinear ODEs suggest that a large set of differentially algebraic power series solutions with integer coefficients might reduce to algebraic functions modulo primes, or powers of primes. Since diagonals of rational functions are well-known to reduce, modulo primes, or powers of primes, to algebraic functions, a large subset of differentially algebraic power series with integer coefficients may be viewed as a natural ‘nonlinear’ generalisation of diagonals of rational functions. Here we give several examples of series with integer coefficients and non-zero radius of convergence that reduce to algebraic functions modulo (almost) every prime (or power of a prime). These examples satisfy differentially algebraic equations with the encoding polynomial occasionally possessing quite high degree (and thus difficult to identify even with long series). These examples shed important light on the very nature of such differentially algebraic series. Additionally, we have extended both the high- and low-temperature Ising square-lattice susceptibility series to 5043 coefficients. We find that even this long series is insufficient to determine whether it reduces to algebraic functions modulo 3, 5, etc. This negative result is in contrast to the comparatively easy confirmation that the corresponding series reduce to algebraic functions modulo powers of 2. Finally we show that even with 5043 terms we are unable to identify an underlying differentially algebraic equation for the susceptibility, ruling out a number of possible differentially algebraic forms.