Low-temperature Series Research Articles

Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice.

In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic–to–paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models.

Mesomorphism dependence on molecular rigidity with reference to ‒CH˭CH‒ unit of central bridge

ABSTRACTA novel ester homologous series of rich mesomorphism and low temperatures with unexpected phase behaviors of eleven homologues was synthesized and studied with a view to understanding and establishing the relation between mesomorphic behaviour and the molecular structure of a series 4-(4′-n-alkoxybenzoyloxy)-4″-chlorobenzyl cinnamates. All the members of the novel series are enantiotropically smectogenic and the octyloxy (C8) to hexadecyloxy (C16) homologues are enantiotropically nematogenic, in addition to smectogenic. Odd–even effect is observed for Sm‒I/Sm‒N transition curve but it is absent for N‒I transition curve. Textures of nematic phase are threaded or Schlieren and that of the smectic phase are fan shaped or batonates of smectic-A type phase or Smectic-C type for C16 homologues as judged directly from a heating stage of an optical polarizing microscopy. Analytical and spectral data confirmed the molecular structures of novel homologues. Mesomorphic properties of present series are compared with the structurally similar other known series. The average smectic and nematic thermal stabilities are 92.78°C and 100.8°C, respectively. Mesophase length minimum to maximum for smectic and nematic are 21.0°C to 31.1°C and 8.4°C to 42.6°C respectively. Thus, the present novel series is partly nematogenic and fully smectogenic with considerable degree of mesomorphism and low melting type.

Assessment of frost damage in mycorrhizal and non-mycorrhizal roots of Scots pine seedlings using classification analysis of their electrical impedance spectra

A novel non-destructive method is presented for studying the frost hardiness of roots. Principal component analysis from the electrical impedance spectra revealed differences between freezing temperatures, but no clear differences between the mycorrhizal treatments as regards freezing stress. We present a novel non-destructive method for the classification of root systems with different degrees of freezing injuries based on the measurement of electrical impedance spectra (EIS). Roots of Scots pine (Pinus sylvestris L.) seedlings, raised in perlite with nutrient solution, were colonized by Hebeloma sp. or Suillus luteus or left non-mycorrhizal, and exposed to a series of low temperatures (5, −5, −12 and −18 °C) after cultivation with and without cold acclimation regimes. In EIS measurements, we ran a small-amplitude electric current to the root system at 44 frequencies between 5 Hz and 100 kHz through electrodes set in the stem and in perlite at the bottom of the container. The normalized (Euclidian) electrical impedance spectra were classified using the CLAFIC-method (CLAss-Featuring Information Compression) that is based on a subspace method with two variants where the longest projection vector defines the sample class. The current delivery through the root system was affected by freezing injuries in the roots. The most remarkable change, indicating the threshold for cold tolerance, took place between −5 and −12 °C for non-acclimated and between −12 and −18 °C for cold acclimated roots. No difference was found between the mycorrhizal treatments in the response to the freezing temperatures. The results on the effects of both the low-temperature exposure and mycorrhizas agree with freezing damage assessments done by other methods.

Thermodynamics of ferromagnetic spin chains in a magnetic field: Impact of the spin–wave interaction

The thermodynamic properties of ferromagnetic spin chains have been the subject of many publications. Still, the problem of how the spin–wave interaction manifest itself in these low-temperature series has been neglected. Using the method of effective Lagrangians, we explicitly evaluate the partition function of ferromagnetic spin chains at low temperatures and in the presence of a magnetic field up to three loops in the perturbative expansion where the spin–wave interaction sets in. We discuss in detail the renormalization and the numerical evaluation of a particular three-loop graph and derive the low-temperature series for the free energy density, energy density, heat capacity, entropy density, as well as the magnetization and the susceptibility. In the low-temperature expansion for the free energy density, the spin–wave interaction starts manifesting itself at order T5/2. In the pressure, the coefficient of the T5/2-term is positive, indicating that the spin–wave interaction is repulsive. While it is straightforward to go up to three-loop order in the effective loop expansion, the analogous calculation on the basis of conventional condensed matter methods, such as spin–wave theory, appears to be beyond reach.

Exact expression for the number of energy states in lattice models

We derive a closed-form combinatorial expression for the number of states in canonical systems with discrete energy levels. The expression results from the exact low-temperature power series expansion of the partition function. The approach provides interesting insights into basis of statistical mechanics. In particular, it is shown that in some cases the logarithm of the partition function may be considered the generating function for the number of internal states of energy clusters, which characterize system's microscopic configurations. Apart from elementary examples including the Poisson, geometric and negative binomial probability distributions for the energy, the framework is also validated against the one-dimensional Ising model.

Magnon energy renormalization and low-temperature thermodynamics of O(3) Heisenberg ferromagnets

We present the perturbation theory for lattice magnon fields of the D-dimensional O(3) Heisenberg ferromagnet. The effective Hamiltonian for the lattice magnon fields is obtained starting from the effective Lagrangian, with two dominant contributions that describe magnon–magnon interactions identified as a usual gradient term for the unit vector field and a part originating in the Wess–Zumino–Witten term of the effective Lagrangian. Feynman diagrams for lattice scalar fields with derivative couplings are introduced, on the basis of which we investigate the influence of magnon–magnon interactions on magnon self-energy and ferromagnet free energy. We also comment appearance of spurious terms in low-temperature series for the free energy by examining magnon–magnon interactions and internal symmetry of the effective Hamiltonian (Lagrangian).

Low-temperature properties of ferromagnetic spin chains in a magnetic field

The thermodynamic properties of ferromagnetic spin chains have been analyzed with a variety of microscopic methods over the years: Bethe ansatz, spin-wave theory, Schwinger-boson mean-field theory, Green functions, and renormalization group methods. Surprisingly, in all these different studies, the manifestation of the spin-wave interaction in the low-temperature series for the thermodynamic quantities, in the presence of a finite magnetic field, has been largely neglected. In the present work, we address this problem by following a different path, based on the systematic effective Lagrangian method. We evaluate the partition function up to two-loop order and derive the low-temperature expansion of the energy density, entropy density, heat capacity, magnetization, and susceptibility in the presence of a weak external magnetic field. Remarkably, the spin-wave interaction only manifests itself beyond two-loop order. In particular, there is no term of order ${T}^{2}$ in the low-temperature series of the free energy density. This is the analog of Dyson's statement that there is no term of order ${T}^{4}$ in the low-temperature series of the free energy density in the case of three-dimensional ideal ferromagnets. The range of validity of our series is critically examined in view of the nonperturbatively generated energy gap. We also compare our results with the condensed matter literature and point out that there are some misleading statements.

Rapid effects of humidity acclimation on stress resistance in Drosophila melanogaster

We tested the hypothesis whether developmental acclimation at ecologically relevant humidity regimes (40% and 75% RH) affects desiccation resistance of pre-adults (3rd instar larvae) and adults of Drosophila melanogaster Meigen (Diptera: Drosophilidae). Additionally, we untangled whether drought (40% RH) acclimation affects cold-tolerance in the adults of D. melanogaster. We observed that low humidity (40% RH) acclimated individuals survived significantly longer (1.6-fold) under lethal levels of desiccation stress (0–5% RH) than their counter-replicates acclimated at 75% RH. In contrast to a faster duration of development of 1st and 2nd instar larvae, 3rd instar larvae showed a delayed development at 40% RH as compared to their counterparts grown at 75% RH. Rearing to low humidity conferred an increase in bulk water, hemolymph content and dehydration tolerance, consistent with increase in desiccation resistance for replicates grown at 40% as compared to their counterparts at 75% RH. Further, we found a trade-off between the levels of carbohydrates and body lipid reserves at 40% and 75% RH. Higher levels of carbohydrates sustained longer survival under desiccation stress for individuals developed at 40% RH than their congeners at 75% RH. However, the rate of carbohydrate utilization did not differ between the individuals reared at these contrasting humidity regimes. Interestingly, our results of accelerated failure time (AFT) models showed substantial decreased death rates at a series of low temperatures (0, −2, or −4°C) for replicates acclimated at 40% RH as compared to their counter-parts at 75% RH. Therefore, our findings indicate that development to low humidity conditions constrained on multiple physiological mechanisms of water-balance, and conferred cross-tolerance towards desiccation and cold stress in D. melanogaster. Finally, we suggest that the ability of generalist Drosophila species to tolerate fluctuations in humidity might aid in their existence and abundance under expected changes in moisture level in course of global climate change.

Risk prediction of low temperature in Nanjing city based on grey weighted Markov model

In this research, we calculate the days whose temperature is less than or equal to −5 °C in a year according to the data of the daily minimum temperature in Nanjing city (China) from 1951 to 2011, divide these days into 6 categories according to the number (one, two, three, four, five, six and above) of consecutive low-temperature days, and introduce a annual low-temperature weighted index series. We divide the 61 annual low-temperature weighted indexes of 1951–2011 into five states using the mean standard deviation method. Based on the observation sequence of state of low-temperature in 1951–2009, we simulate the real low-temperature states of 2010 and 2011 by employing both weighted Markov method and grey weighted Markov method. The results of both methods show that the values of simulation (predicted) state agree with those of real state. Based on the state series of low temperature in 1951–2011, we predict the future state of low temperature of Nanjing city in 2012 by utilizing both weighted Markov method and grey weighted Markov method. It is found that the risk of low temperature belongs to the third state when we use weighted Markov method; however, the risk of low temperature belongs to the second state when we use the latter method. Although the states of the risk of low temperature are different because they are predicted by different methods, the two states illustrate that the risk of low temperature of Nanjing city in 2012 is in a normal situation.

Long Wavelength Low Temperature Grown GaAs and InP-Based Terahertz Photoconductors Devices

A series of molecular beam epitaxy low temperature grown structures with various epitaxial and doping profiles are studied, and photoconductive antennas made on these structures are evaluated in a time-domain spectroscopy system. The structures are synthesized to absorb light at wavelengths of 800 nm, and 1 and 1.55 μm. Apertures and dipoles are designed as photoconductive antennas. The key findings for the long wavelength devices (1.55 μm) demonstrate materials with very short carrier lifetimes ( <; 1 ps), high resistivity ( >; 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> Ω/sq) , and system responses with THz pulses having power-to-noise ratio of 50 dB or more. These characteristics are among the best ever reported for such material systems, making them efficient THz emitters and detectors for various optoelectronic applications, especially for telecom laser-driven continuous wave THz systems.

Thermodynamics of two-dimensional ideal ferromagnets: Three-loop analysis

Within the effective Lagrangian framework, we explicitly evaluate the partition function of two-dimensional ideal ferromagnets up to three loops at low temperatures and in the presence of a weak external magnetic field. The low-temperature series for the free energy density, energy density, heat capacity, entropy density, and magnetization are given and their range of validity is critically examined in view of the Mermin-Wagner theorem. The calculation involves the renormalization and numerical evaluation of a particular three-loop graph, which is discussed in detail. Interestingly, in the low-temperature series for the two-dimensional ideal ferromagnet, the spin-wave interaction manifests itself in the form of logarithmic terms. In the free energy density the leading such term is of order ${T}^{4}\mathrm{ln}T$: remarkably, in the case of the three-dimensional ideal ferromagnet no logarithmic terms arise in the low-temperature series. While the present study demonstrates that it is straightforward to consider effects up to three-loop order in the effective field theory framework, this precision seems to be far beyond the reach of microscopic methods such as spin-wave theory.

Low-temperature properties of two-dimensional ideal ferromagnets

The manifestation of the spin-wave interaction in the low-temperature series of the partition function has been investigated extensively over more than seven decades in the case of the three-dimensional ferromagnet. Surprisingly, the same problem regarding ferromagnets in two spatial dimensions, to the best of our knowledge, has never been addressed in a systematic way so far. In the present paper the low-temperature properties of two-dimensional ideal ferromagnets are analyzed within the model-independent method of effective Lagrangians. The low-temperature expansion of the partition function is evaluated up to two-loop order and the general structure of this series is discussed, including the effect of a weak external magnetic field. Our results apply to two-dimensional ideal ferromagnets which exhibit a spontaneously broken spin rotation symmetry O(3) $\to $ O(2) and are defined on a square, honeycomb, triangular or Kagom\'e lattice. Remarkably, the spin-wave interaction only sets in at three-loop order. In particular, there is no interaction term of order $T^3$ in the low-temperature series for the free energy density. This is the analog of the statement that, in the case of three-dimensional ferromagnets, there is no interaction term of order $T^4$ in the free energy density. We also provide a careful discussion of the implications of the Mermin-Wagner theorem in the present context and thereby put our low-temperature expansions on safe grounds.

The surface blistering kinetics and the H-platelet evolution in H-implanted germanium

The surface blistering phenomenon produced in H-implanted Ge by a series of low temperature annealing processes was investigated. The kinetic plot of the onset of blistering contains a break point that separates the straight-line plot into two parts, with two distinct slopes based on the calculated activation energy from the different temperature regions for 3×1016cm−2 and 5×1016cm−2 H-implanted doses. This plot indicates the existence of distinct, temperature dependent mechanisms, probably caused by the release of different types of H-platelets. The turning direction (from low to high temperature) of the Arrhenius plot with the break point is contrary to that of other known materials. The formation and evolution of the H-platelets under the Ge surface was revealed by TEM (transmission electron microscopy). The TEM results demonstrate that the 〈001〉 platelets parallel to the sample surface are first produced by a low H implantation dose; however, the vertical 〈010〉 platelets perpendicular to the sample surface form later as the H implantation dose increases. The H-platelets combine with each other, becoming micro-cracks. The {111} and {311} micro-cracks serve as interconnections between the 〈001〉-oriented micro-cracks below the substrate surface. Finally, the accumulated H2 pressure in the cracks deforms the surface to generate Ge surface exfoliation.

Series Analysis of a Kosterlitz-Thouless Transition: The 6-State Planar Potts Model

A new implementation of the Finite Lattice Method of series expansion is used to derive low temperature series for the 6-state planar Potts model. This is expected to have Kosterlitz-Thouless transitions between the ordered low-temperature phase and a massless phase, and between the massless phase and a high-temperature disordered phase. In an exploratory study, we have analysed series for the order parameter to order x59. These series have proved particularly difficult to analyse and when seeking to both locate the transition and confirm the form of the Kosterlitz-Thouless transition, considerable ambiguity is found. If however the form of the Kosterlitz-Thouless transition is assumed, then the series analysis consistently indicates that the lower transition occurs at xL=0.4886(10). A more conservative analysis, which made no assumption about the nature of the transition, led to the estimate xL=0.485(8).

Formation of H2 and CH4 by weathering of olivine at temperatures between 30 and 70°C.

Hydrocarbons such as CH4 are known to be formed through the Fischer-Tropsch or Sabatier type reactions in hydrothermal systems usually at temperatures above 100°C. Weathering of olivine is sometimes suggested to account for abiotic formation of CH4 through its redox lowering and water splitting properties. Knowledge about the CH4 and H2 formation processes at low temperatures is important for the research about the origin and cause of early Earth and Martian CH4 and for CO2 sequestration. We have conducted a series of low temperature, long-term weathering experiments in which we have tested the CH4 and H2 formation potential of forsteritic olivine.The results show low temperature CH4 production that is probably influenced by chromite and magnetite as catalysts. Extensive analyses of a potential CH4 source trapped in the crystal structure of the olivine showed no signs of incorporated CH4. Also, the available sources of organic carbon were not enough to support the total amount of CH4 detected in our experiments. There was also a linear relationship between silica release into solution and the net CH4 accumulation into the incubation bottle headspaces suggesting that CH4 formation under these conditions could be a qualitative indicator of olivine dissolution.It is likely that minerals such as magnetite, chromite and other metal-rich minerals found on the olivine surface catalyze the formation of CH4, because of the low temperature of the system. This may expand the range of environments plausible for abiotic CH4 formation both on Earth and on other terrestrial bodies.

Universal amplitude ratios in the three-dimensional Ising universality class

We compute a number of universal amplitude ratios in the three-dimensional Ising universality class. To this end, we perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. For example, we obtain A_+/A_-=0.536(2) and C_+/C_-=4.713(7), where A_+- and C_+- are the amplitudes of the specific heat and the magnetic susceptibility, respectively. The subscripts + and - indicate the high and the low temperature phase, respectively. We compare our results with those obtained from previous Monte Carlo simulations, high and low temperature series expansions, field theoretic methods and experiments.

Honeycomb-Lattice Ising Model in Nonzero Magnetic Field: Low-Temperature Series Analysis and Partition Function Zeros

Honeycomb-Lattice Ising Model in Nonzero Magnetic Field: Low-Temperature Series Analysis and Partition Function Zeros

Thermodynamics ofO(N)antiferromagnets in2+1dimensions

Within the framework of effective Lagrangians we calculate the free energy density for an O($N$) antiferromagnet in 2+1 dimensions up to three-loop order in the perturbative expansion and derive the low-temperature series for various thermodynamic quantities. In particular, we show that the magnon-magnon interaction in the O(3) antiferromagnet in $d$=2+1 -- the O(3)-invariant quantum Heisenberg antiferromagnet on a square or a honeycomb lattice -- is very weak and repulsive and manifests itself through a term proportional to five powers of the temperature in the free energy density. Remarkably, the corresponding coefficient is fully determined by the leading-order effective Lagrangian ${\cal L}^2_{eff}$ and does not involve any higher order effective constants from ${\cal L}^4_{eff}$ related to the anisotropies of the lattice -- the symmetries are thus very restrictive in $d$=2+1. We also compare our results that apply to O($N$) antiferromagnets in 2+1 dimensions with the those for O($N$) antiferromagnets in 3+1 dimensions. The present work demonstrates the efficiency of the fully systematic effective Lagrangian method in the condensed matter domain, which clearly proves to be superior to spin-wave theory. We would like to emphasize that the structure of the low-temperature series derived in the present work is model-independent and universal as it only relies on symmetry considerations.

Spontaneous magnetization of the square 2D Ising lattice with nearest- and weak next-nearest-neighbour interactions

We show that the square two-dimensional (2D) Ising lattice with nearest- (J) and weak next-nearest-neighbour interactions (Jd ) can be mapped on a square 2D Ising lattice that has only nearest neighbour interactions (J*). For J d /J << 1 the transformation equation has the simple form . This result can be used to derive expressions for several thermodynamic functions of the square 2D Ising lattice with weak next-nearest-neighbour interactions. As an example we consider the spontaneous magnetization and compare it with low-temperature series expansion results.

Inverse melting in lattice-gas models

Inverse melting is the phenomenon, observed in both helium isotopes, by which a crystal melts when cooled at constant pressure. I investigate discrete-space analogs of inverse melting by means of two instances of a triangular-lattice-gas system endowed with a soft-core repulsion and a short-ranged attraction. To reconstruct the phase diagram, I use both transfer-matrix and Monte Carlo methods, as well as low-temperature series expansions. In one case, a phase behavior reminiscent of helium emerges, with a loose-packed phase (which is solidlike for low temperatures and liquidlike for high temperatures) extending down to zero temperature for low pressures and the possibility of melting the close-packed solid by isobaric cooling. At variance with previous model studies of inverse melting, the driving mechanism of the present phenomenon is mainly geometrical, related to the larger free-energy cost of a "vacancy" in the loose-packed solid than in the close-packed one.