THE EXACT SOLUTION OF SOME LATTICE STATISTICS MODELS WITH FOUR STATES PER SITE

1964 ◽  
Vol 42 (8) ◽  
pp. 1564-1572 ◽  
Author(s):  
D. D. Betts
Keyword(s):  
Partition Function ◽  
Nearest Neighbor ◽  
Quaternary Alloy ◽  
Interesting Property ◽  
Two Dimensions ◽  
Lattice Statistics ◽  
Critical Temperatures ◽  
Different Types ◽  
Interacting Systems ◽  
Statistical Mechanical

Statistical mechanical ensembles of interacting systems localized at the sites of a regular lattice and each having four possible states are considered. A set of lattice functions is introduced which permits a considerable simplification of the partition function for general nearest-neighbor interactions. The particular case of the Potts four-state ferromagnet model is solved exactly in two dimensions. The order–disorder problem for a certain quaternary alloy model is also solved exactly on a square net. The quaternary alloy model has the interesting property that it has two critical temperatures and exhibits two different types of long-range order. The partition function for the spin-3/2 Ising model on a square net is expressed in terms of graphs without odd vertices, but has not been solved exactly.

scholarly journals Exact Solution for Three-Dimensional Ising Model

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1837
Author(s):  
Degang Zhang
Keyword(s):  
Boundary Condition ◽  
Ising Model ◽  
Partition Function ◽  
Operator Algebras ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Critical Temperatures ◽  
Cubic Crystal ◽  
Infinite Crystal ◽  
Analytical Expressions

The three-dimensional Ising model in a zero external field is exactly solved by operator algebras, similar to the Onsager’s approach in two dimensions. The partition function of the simple cubic crystal imposed by the periodic boundary condition along two directions and the screw boundary condition along the third direction is calculated rigorously. In the thermodynamic limit an integral replaces a sum in the formula of the partition function. The critical temperatures, at which order–disorder transitions in the infinite crystal occur along three axis directions, are determined. The analytical expressions for the internal energy and the specific heat are also presented.

THERMAL ZIPPER: IDEALIZED STATISTICAL MECHANICS OF CRACK FORMATION

2001 ◽  
Vol 15 (11) ◽  
pp. 323-330
Author(s):  
DANIEL C. MATTIS
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Crack Formation ◽  
Nearest Neighbor ◽  
Two Dimensions ◽  
Coordination Numbers

Cracks are known to form easily along certain crystallographic directions, presumably because of weaker bonds or lower coordination numbers along those directions. We uncover the manner in which such weak bonds break as the temperature is raised, by evaluating the partition function of an anisotropic grid in two dimensions of atoms with nearest-neighbor bonds.

Interionic Pair Potential, hard sphere diameter and entropy of mixing of NaCd compound forming binary molten alloys under the framework of Pseudopotential theory

2014 ◽  
Vol 10 (6) ◽  
pp. 2843-2852
Author(s):  
Sujeet Kumar Chatterjee ◽  
Lokesh Chandra Prasad ◽  
Ajaya Bhattarai
Keyword(s):  
Nearest Neighbor ◽  
Effective Interaction ◽  
Pair Potential ◽  
Sphere Diameter ◽  
Compound Formation ◽  
Pseudopotential Theory ◽  
Energy Of Mixing ◽  
Asymmetric Behaviour ◽  
Statistical Mechanical ◽  
Free Energy Of Mixing

The observed asymmetric behaviour of mixing of  NaCd liquid alloys around equiatomic composition with smaller negative values for free energy of mixing at compound forming concentration, i.e. GMXS = -4.9KJ at Ccd =0.66 has  aroused our interest to undertake a theoretical investigation of this system.A simple statistical mechanical theory based on compound formation model has been used to investigate the energetics of formation of intermetallic compound Cd2Na in the melt through the study of entropy of mixing.Besides, the interionic interactions between component atoms Na and Cd of the alloys have been understood through the study of interionic pair potential фij(r), calculated from pseudopotential theory in the light of CF model.Our study of фij(r) suggest that the effective interaction between Na-Na atoms decreases on alloying with Cd atom, being minimum for compound forming alloy( Cd 0.66 Na 0.34 ).The nearest neighbor distance between Na-Na atoms does not alter on alloying. Like wise Na-Na,  effective interaction between  Cd-Cd atom decreases from pure state to NaCd alloys, being smaller at compound forming  concentration Cd 0.66 Na 0.34.The computed values of SM from pseudopotential theory are positive at all concentrations, but the agreement between theory and experimental is not satisfactory. This might be happening due to parameterisation of σ3 and Ψcompound.

Transition Times in Memory

2018 ◽  
Author(s):  
Donatella della Porta ◽  
Massimiliano Andretta ◽  
Tiago Fernandes ◽  
Eduardo Romanos ◽  
Markos Vogiatzoglou
Keyword(s):  
Theoretical Model ◽  
Social Movement ◽  
Transition Period ◽  
Two Dimensions ◽  
Democratic Regime ◽  
Organizational Models ◽  
Different Types ◽  
Transition Times ◽  
Movement Participation

The second chapter covers the main characteristics of transition time in the four countries: Italy, Greece, Spain, and Portugal. After developing the theoretical model on paths of transition, with a focus on social movement participation, the chapter looks at social movements and protest events as turning points during transition, covering in particular the specific movement actors, their organizational models, and their repertoires of action and frames. The chapter focuses on two dimensions: the role of mobilization in the transition period, which implies the analysis of how elites and masses interact, ally, or fight with each other in the process, and the outcome of transitions as continuity versus rupture of the democratic regime vis-à-vis the old one. It concludes by elaborating some hypotheses on how different modes of transition may produce different types and uses of (transition) memories.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Preschoolers' Imaginativeness: Subtypes, Correlates, and Maladaptive Extremes

1985 ◽  
Vol 4 (4) ◽  
pp. 349-364 ◽  
Author(s):  
Roni Beth Tower
Keyword(s):  
Preschool Children ◽  
Child Development ◽  
Healthy Child ◽  
Observational Studies ◽  
Two Dimensions ◽  
Different Types ◽  
Research Questions ◽  
Negative Implication

In a study of forty-three preschool children, ratings of four types of the children's imaginativeness were correlated with observational, behavioral, and interview measures. Research questions were: 1) Do correlates of imaginativeness found in observational studies replicate if trait rather than state measures are examined? 2) Do different types of imaginativeness have different correlates? and 3) What characteristics distinguish children at the maladaptive extremes of imaginativeness from those at more moderate levels? The conceptual and empirical utility of considering imaginativeness to have two dimensions, Expressive and Constructive, was demonstrated. While optimal levels of Constructive Imaginativeness correlated significantly with other indices of healthy child development, the correlations were fewer and tended to be weaker for Expressive Imaginativeness. The negative implication of extremes was documented.

scholarly journals Cell Bioprinting: The 3D-Bioplotter™ Case

Materials ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 4005 ◽  
Author(s):  
Angelats Lobo ◽  
Ginestra
Keyword(s):  
3D Structure ◽  
Three Dimensional ◽  
Petri Dish ◽  
Two Dimensions ◽  
Point Of View ◽  
Lack Of Information ◽  
Synthetic Materials ◽  
Different Types ◽  
Available Information ◽  
User Friendly

The classic cell culture involves the use of support in two dimensions, such as a well plate or a Petri dish, that allows the culture of different types of cells. However, this technique does not mimic the natural microenvironment where the cells are exposed to. To solve that, three-dimensional bioprinting techniques were implemented, which involves the use of biopolymers and/or synthetic materials and cells. Because of a lack of information between data sources, the objective of this review paper is, to sum up, all the available information on the topic of bioprinting and to help researchers with the problematics with 3D bioprinters, such as the 3D-Bioplotter™. The 3D-Bioplotter™ has been used in the pre-clinical field since 2000 and could allow the printing of more than one material at the same time, and therefore to increase the complexity of the 3D structure manufactured. It is also very precise with maximum flexibility and a user-friendly and stable software that allows the optimization of the bioprinting process on the technological point of view. Different applications have resulted from the research on this field, mainly focused on regenerative medicine, but the lack of information and/or the possible misunderstandings between papers makes the reproducibility of the tests difficult. Nowadays, the 3D Bioprinting is evolving into another technology called 4D Bioprinting, which promises to be the next step in the bioprinting field and might promote great applications in the future.

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