scholarly journals Active-absorbing phase transition and small-world behaviour in Ising model on finite addition type networks in two dimensions

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Pratik Mullick ◽  
Parongama Sen
Keyword(s):  
Ising Model ◽  
Small World ◽  
Fixed Number ◽  
Two Dimensions ◽  
Square Lattice ◽  
Rich Phase ◽  
Different Types ◽  
Two Parameters ◽  
Absorbing States ◽  
Absorbing Phase Transition

Abstract We consider the ordering dynamics of the Ising model on a square lattice where an additional fixed number of bonds connect any two sites chosen randomly from a total of $N$ lattice sites. The total number of shortcuts added is controlled by two parameters $p$ and $\alpha$ for fixed $N$. The structural properties of the network are investigated which show that the small-world behaviour is obtained along the line $\alpha=\frac{\ln (N/2p)}{\ln N}$, which separates regions with ultra-small world like behaviour and short-ranged lattice like behaviour. We obtain a rich phase diagram in the $p-\alpha$ plane showing the existence of different types of active and absorbing states to which the Ising model evolves to and their boundaries.

scholarly journals A comparative study of 2d Ising model at different boundary conditions using Cellular Automata

2018 ◽  
Vol 29 (08) ◽  
pp. 1850066
Author(s):  
Jahangir Mohammed ◽  
Swapna Mahapatra
Keyword(s):  
Ising Model ◽  
Cellular Automata ◽  
Boundary Conditions ◽  
Initial Conditions ◽  
Spontaneous Magnetization ◽  
Spin Systems ◽  
Square Lattice ◽  
Random Orientation ◽  
Lattice Size ◽  
Different Types

Using Cellular Automata, we simulate spin systems corresponding to [Formula: see text] Ising model with various kinds of boundary conditions (bcs). The appearance of spontaneous magnetization in the absence of magnetic field is studied with a [Formula: see text] square lattice with five different bcs, i.e. periodic, adiabatic, reflexive, fixed ([Formula: see text] or [Formula: see text]) bcs with three initial conditions (all spins up, all spins down and random orientation of spins). In the context of [Formula: see text] Ising model, we have calculated the magnetization, energy, specific heat, susceptibility and entropy with each of the bcs and observed that the phase transition occurs around [Formula: see text] as obtained by Onsager. We compare the behavior of magnetization versus temperature for different types of bcs by calculating the number of points close to the line of zero magnetization after [Formula: see text] at various lattice sizes. We observe that the periodic, adiabatic and reflexive bcs give closer approximation to the value of [Formula: see text] than fixed [Formula: see text] and fixed [Formula: see text] bcs with all three initial conditions for lattice sizes less than [Formula: see text]. However, for lattice size between [Formula: see text] and [Formula: see text], fixed [Formula: see text] bc and fixed [Formula: see text] bc give closer approximation to the [Formula: see text] with initial conditions all spin down configuration and all spin up configuration, respectively.

FRUSTRATION EFFECTS ON SMALL-WORLD NETWORKS

2004 ◽  
Vol 15 (09) ◽  
pp. 1269-1277 ◽  
Author(s):  
PAULO R. A. CAMPOS ◽  
VIVIANE M. DE OLIVEIRA ◽  
F. G. BRADY MOREIRA
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Critical Behavior ◽  
Magnetic Ordering ◽  
Small World ◽  
Two Dimensions ◽  
Small World Networks ◽  
Ferromagnetic Ising Model ◽  
Antiferromagnetic Ising Model ◽  
Frustration Effects

We investigate the frustration effects on small-world networks by studying antiferromagnetic Ising model in two dimensions. When the rewiring is constrained to those sites such that the interaction still occurs between spins in distinct sublattices and frustration does not take place, we observe that the system behaves as in previous investigations of ferromagnetic Ising model. However, when the rewiring procedure does not only produce interactions between spins in distinct sublattices, small-world configurations can effectively produce geometrical frustration and we attain a different critical behavior. In the frustrated case, the critical temperature decreases with the augment of the rewiring probability and the magnetic ordering presents two different regimes for low and high p.

Ising model critical exponent η from a criticality equation

1989 ◽  
Vol 67 (10) ◽  
pp. 946-951 ◽  
Author(s):  
B. Frank ◽  
L. Macot ◽  
K. V. Bassias ◽  
M. Danino
Keyword(s):  
Ising Model ◽  
Critical Exponent ◽  
Pair Correlation ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Square Lattice ◽  
Specific Method ◽  
Hamiltonian Methods ◽  
Order Of Magnitude

A pair-correlation function ansatz, previously used in the derivation of the Ising model critical exponent η for the square lattice from a criticality equation within the i-δ approximation, is investigated further. Various methods are used to calculate the multispin correlation functions entering the criticality equation. The calculations are extended to the three-dimensional cubic lattices. It is found that the values obtained for η are relatively insensitive to the specific method used. In two dimensions, η takes the values 0.2506 (i-δ method), 0.2471, and 0.2490 (renormalized Hamiltonian methods), thereby remaining within 1.2% of the exact value 1/4. In three dimensions, η ranges from 0.030 to 0.075, being of the same order of magnitude as the series value 0.041 ± 0.01.

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.

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.

TRANSFER-MATRIX STUDY OF NEGATIVE-FUGACITY SINGULARITY OF HARD-CORE LATTICE GAS

1999 ◽  
Vol 10 (04) ◽  
pp. 517-529 ◽  
Author(s):  
SYNGE TODO
Keyword(s):  
Large Scale ◽  
Lattice Gas ◽  
Central Charge ◽  
Hard Core ◽  
Universality Class ◽  
Two Dimensions ◽  
Square Lattice ◽  
Lattice Gas Models ◽  
Renormalization Technique ◽  
Phenomenological Renormalization

A singularity on the negative-fugacity axis of the hard-core lattice gas is investigated in terms of numerical diagonalization of large-scale transfer matrices. For the hard-square lattice gas, the location of the singular point [Formula: see text] and the critical exponent ν are accurately determined by the phenomenological renormalization technique as -0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge c and the dominant scaling dimension xσ are -4.399996(8) and -0.3999996(7), respectively. Similar analyses for other hard-core lattice-gas models in two dimensions are also performed, and it is confirmed that the universality between these models does hold. These results strongly indicate that the present singularity belongs to the same universality class as the Yang–Lee edge singularity.

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 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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