Neste trabalho consideramos três modelos de Ising com competição: que é gerada por acoplamentos dinâmicos de caráter antagônicos, pela própria geometria da rede subjacente ou através de interações de periodicidades uniaxiais competitivas e elementos de desordem. O primeiro modelo, no qual as técnicas de mecânica estatística de equilíbrio não se aplicam, consiste numa rede neural atratora completamente conectada com acoplamentos assimétricos armazenando p = 2 padrões, cuja evolução temporal pode ser descrita (no caso de atualização síncrona) por um mapeamento dissipativo bidimensional. O segundo modelo se refere ao problema clássico do antiferromagneto de Ising na rede triangular na presença de um campo magnético uniforme, investigado através de diversas aproximações - em particular, através de uma aproximação de Bethe-Peierls considerando três sub-redes interpenetrantes equivalentes. O terceiro modelo, introduzido para investigar o efeito de uma desordem congelada em um sistema magnético modulado, é definido pelo modelo ANNNI em um campo aleatório. Inicialmente consideramos um análogo deste modelo na árvore de Cayley, no limite de coordenação infinita, que pode ser formulado em termos de um mapeamento dissipativo bidimensional. A seguir, consideramos uma versão de campo médio em uma rede cúbica simples. que permite uma análise das superfícies de transição de primeira ordem e das linhas tricriticas. / In this work we consider three Ising models with competition: which is generated by dynamical couplings of antagonistic character, by the geometry of the underlying lattice, or by interactions of competitive uniaxial periodicities and disorder elements. The first model, for which equilibrium statistical mechanics techniques do not apply, consists in a fully connected attractor neural network storing p = 2 patterns, whose temporal evolution can be described (in the case of synchronous updating) by a two-dimensional dissipative mapping. The second model refers to the classic problem of the Ising antiferromagnet on the triangular lattice in the presence of a uniform magnetic field, which is investigated by various approximations - in particular, by a Bethe-Peierls approximation considering three interpenetrating equivalent sublattices. The third model, introduced to investigate the effects of quenched disorder in a modulated magnetic system, is defined by the ANNNI model in a random field. Initially we consider an analogous of this model on a Cayley tree, in the infinite-coordination limit, which can be formulated in terms of a two-dimensional dissipative mapping. Next, we consider a mean-field version on a simple cubic lattice, which allows for an analysis of the first-order transition surfaces and tricritical lines.

Neste trabalho consideramos três modelos de Ising com competição: que é gerada por acoplamentos dinâmicos de caráter antagônicos, pela própria geometria da rede subjacente ou através de interações de periodicidades uniaxiais competitivas e elementos de desordem. O primeiro modelo, no qual as técnicas de mecânica estatística de equilíbrio não se aplicam, consiste numa rede neural atratora completamente conectada com acoplamentos assimétricos armazenando p = 2 padrões, cuja evolução temporal pode ser descrita (no caso de atualização síncrona) por um mapeamento dissipativo bidimensional. O segundo modelo se refere ao problema clássico do antiferromagneto de Ising na rede triangular na presença de um campo magnético uniforme, investigado através de diversas aproximações - em particular, através de uma aproximação de Bethe-Peierls considerando três sub-redes interpenetrantes equivalentes. O terceiro modelo, introduzido para investigar o efeito de uma desordem congelada em um sistema magnético modulado, é definido pelo modelo ANNNI em um campo aleatório. Inicialmente consideramos um análogo deste modelo na árvore de Cayley, no limite de coordenação infinita, que pode ser formulado em termos de um mapeamento dissipativo bidimensional. A seguir, consideramos uma versão de campo médio em uma rede cúbica simples. que permite uma análise das superfícies de transição de primeira ordem e das linhas tricriticas. / In this work we consider three Ising models with competition: which is generated by dynamical couplings of antagonistic character, by the geometry of the underlying lattice, or by interactions of competitive uniaxial periodicities and disorder elements. The first model, for which equilibrium statistical mechanics techniques do not apply, consists in a fully connected attractor neural network storing p = 2 patterns, whose temporal evolution can be described (in the case of synchronous updating) by a two-dimensional dissipative mapping. The second model refers to the classic problem of the Ising antiferromagnet on the triangular lattice in the presence of a uniform magnetic field, which is investigated by various approximations - in particular, by a Bethe-Peierls approximation considering three interpenetrating equivalent sublattices. The third model, introduced to investigate the effects of quenched disorder in a modulated magnetic system, is defined by the ANNNI model in a random field. Initially we consider an analogous of this model on a Cayley tree, in the infinite-coordination limit, which can be formulated in terms of a two-dimensional dissipative mapping. Next, we consider a mean-field version on a simple cubic lattice, which allows for an analysis of the first-order transition surfaces and tricritical lines.

<p>In this thesis we present a model of the interacting agents on the financial market. The agents are represented by a non-Euclidean random graph, where each agent communicate with another with probability p, and the interaction according to the Ising Model. We investigate properties of the model by direct calculations for small graph sizes, and by perfect simulation for larger graph sizes. We also present a model for asset price variation by using the magnetization of the Ising model.</p>

The phase transitions of a newly proposed torsion X-Y model, are studied with molecular dynamics. ForJ3 >0, the influence from J1 term is similar to the term.We found the Torsion X-Y Model and X-Y Model or Coupled X-Y Model all have the Kosterlitz-Thouless transition. (KT) We also confirm that the KT transition is a second order transition , The distribution of angle £c start from dis-ordered to well-ordered. KT starts first before the randomly distributed £c shows preference and ends when the preference is merged. For the J3 <0 case, the KT is also found in J3=-0.0167 and J3=-0.0334 The temperature for negative J3 is lower then that for positive J3 due to the resistant force to £c ordering from the coupled interaction.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 55-58). Also available in electronic version. Access restricted to campus users.

No description available.

Neurons, the building blocks of the brain, are an astonishingly capable type of cell. Collectively they can store, manipulate and retrieve biologically important information, allowing animals to learn and adapt to environmental changes. This universal adaptability is widely believed to be due to plasticity: the readiness of neurons to manipulate and adjust their intrinsic properties and strengths of connections to other cells. It is through such modifications that associations between neurons can be made, giving rise to memory representations; for example, linking a neuron responding to the smell of pancakes with neurons encoding sweet taste and general gustatory pleasure. However, this malleability inherent to neuronal cells poses a dilemma from the point of view of stability: how is the brain able to maintain stable operation while in the state of constant flux? First of all, won’t there occur purely technical problems akin to short-circuiting or runaway activity? And second of all, if the neurons are so easily plastic and changeable, how can they provide a reliable description of the environment? Of course, evidence abounds to testify to the robustness of brains, both from everyday experience and scientific experiments. How does this robustness come about? Firstly, many control feedback mechanisms are in place to ensure that neurons do not enter wild regimes of behaviour. These mechanisms are collectively known as homeostatic plasticity, since they ensure functional homeostasis through plastic changes. One well-known example is synaptic scaling, a type of plasticity ensuring that a single neuron does not get overexcited by its inputs: whenever learning occurs and connections between cells get strengthened, subsequently all the neurons’ inputs get downscaled to maintain a stable level of net incoming signals. And secondly, as hinted by other researchers and directly explored in this work, networks of neurons exhibit a property present in many complex systems called sloppiness. That is, they produce very similar behaviour under a wide range of parameters. This principle appears to operate on many scales and is highly useful (perhaps even unavoidable), as it permits for variation between individuals and for robustness to mutations and developmental perturbations: since there are many combinations of parameters resulting in similar operational behaviour, a disturbance of a single, or even several, parameters does not need to lead to dysfunction. It is also that same property that permits networks of neurons to flexibly reorganize and learn without becoming unstable. As an illustrative example, consider encountering maple syrup for the first time and associating it with pancakes; thanks to sloppiness, this new link can be added without causing the network to fire excessively. As has been found in previous experimental studies, consistent multi-neuron activity patterns arise across organisms, despite the interindividual differences in firing profiles of single cells and precise values of connection strengths. Such activity patterns, as has been furthermore shown, can be maintained despite pharmacological perturbation, as neurons compensate for the perturbed parameters by adjusting others; however, not all pharmacological perturbations can be thus amended. In the present work, it is for the first time directly demonstrated that groups of neurons are by rule sloppy; their collective parameter space is mapped to reveal which are the sensitive and insensitive parameter combinations; and it is shown that the majority of spontaneous fluctuations over time primarily affect the insensitive parameters. In order to demonstrate the above, hippocampal neurons of the rat were grown in culture over multi-electrode arrays and recorded from for several days. Subsequently, statistical models were fit to the activity patterns of groups of neurons to obtain a mathematically tractable description of their collective behaviour at each time point. These models provide robust fits to the data and allow for a principled sensitivity analysis with the use of information-theoretic tools. This analysis has revealed that groups of neurons tend to be governed by a few leader units. Furthermore, it appears that it was the stability of these key neurons and their connections that ensured the stability of collective firing patterns across time. The remaining units, in turn, were free to undergo plastic changes without risking destabilizing the collective behaviour. Together with what has been observed by other researchers, the findings of the present work suggest that the impressively adaptable yet robust functioning of the brain is made possible by the interplay of feedback control of few crucial properties of neurons and the general sloppy design of networks. It has, in fact, been hypothesised that any complex system subject to evolution is bound to rely on such design: in order to cope with natural selection under changing environmental circumstances, it would be difficult for a system to rely on tightly controlled parameters. It might be, therefore, that all life is just, by nature, sloppy.

Neste trabalho apresentamos alguns resultados da invariância conforme e da teoria de escala para sistemas finitos. Estudamos, usando tais técnicas, dois modelos estatísticos (modelos 1 e 2). Para cada modelo obtivemos a anomalia conforme e as dimensões dos operadores energia e magnetização bem como seus respectivos descendentes / In this work we show some results of conformal invariance theory and finite-size scaling. We study by using these theories two statistical mechanics models (models 1 and 2). To each model we obtained the conformal anomaly, the dimensions of energy and magnetization operators as well their respective descendents

A multivariate generalization of mutual information, multi-information, is defined in the thermodynamic limit. The definition takes phase coexistence into account by taking the infimum over the translation-invariant Gibbs measures of an interaction potential. It is shown that this infimum is attained in a pure state. An explicit formula can be found for the Ising square lattice, where the quantity is proved to be maximized at the phase-transition point. By this, phase coexis-tence is linked to high model complexity in a rigorous way.

In this thesis we present a model of the interacting agents on the financial market. The agents are represented by a non-Euclidean random graph, where each agent communicate with another with probability p, and the interaction according to the Ising Model. We investigate properties of the model by direct calculations for small graph sizes, and by perfect simulation for larger graph sizes. We also present a model for asset price variation by using the magnetization of the Ising model.