Tunneling behavior of Ising and Potts models in the low-temperature regime

We consider the ferromagnetic $q$-state Potts model with zero external field in a finite volume and assume that the stochastic evolution of this system is described by a Glauber-type dynamics parametrized by the inverse temperature $\beta$. Our analysis concerns the low-temperature regime $\beta \to \infty$, in which this multi-spin system has $q$ stable equilibria, corresponding to the configurations where all spins are equal. Focusing on grid graphs with various boundary conditions, we study the tunneling phenomena of the $q$-state Potts model. More specifically, we describe the asymptotic behavior of the first hitting times between stable equilibria as $\beta \to \infty$ in probability, in expectation, and in distribution and obtain tight bounds on the mixing time as side-result. In the special case $q=2$, our results characterize the tunneling behavior of the Ising model on grid graphs.Comment: 13 figure

Asymptotically exponential hitting times and metastability: a pathwise approach without reversibility

We study the hitting times of Markov processes to target set $G$, starting from a reference configuration $x_0$ or its basin of attraction. The configuration $x_0$ can correspond to the bottom of a (meta)stable well, while the target $G$ could be either a set of saddle (exit) points of the well, or a set of further (meta)stable configurations. Three types of results are reported: (1) A general theory is developed, based on the path-wise approach to metastability, which has three important attributes. First, it is general in that it does not assume reversibility of the process, does not focus only on hitting times to rare events and does not assume a particular starting measure. Second, it relies only on the natural hypothesis that the mean hitting time to $G$ is asymptotically longer than the mean recurrence time to $x_0$ or $G$. Third, despite its mathematical simplicity, the approach yields precise and explicit bounds on the corrections to exponentiality. (2) We compare and relate different metastability conditions proposed in the literature so to eliminate potential sources of confusion. This is specially relevant for evolutions of infinite-volume systems, whose treatment depends on whether and how relevant parameters (temperature, fields) are adjusted. (3) We introduce the notion of early asymptotic exponential behavior to control time scales asymptotically smaller than the mean-time scale. This control is particularly relevant for systems with unbounded state space where nucleations leading to exit from metastability can happen anywhere in the volume. We provide natural sufficient conditions on recurrence times for this early exponentiality to hold and show that it leads to estimations of probability density functions

A conversation with 590 nascent entrepreneurs

This paper summarizes interviews from 1998 with 590 individuals trying to create a business centered around five questions: “Who are you?”, “What are you trying to accomplish?”, “What have you and others put into the business?”, “What have you accomplished?”, “What remains to be done?” There is a great deal of heterogeneity across these Nascent entrepreneurs, but they tend to have more education than the general population. Growing up in a family in which one or both parents had a business does not seem to be an important determinant of entry into entrepreneurship for males, while it seems to be of some importance for females. Most of the nascent businesses are in retail and consumer services, and about 50 percent of nascent entrepreneurs expect to become employers within five years of the business’s birth. Most nascent entrepreneurs have already made personally-significant investments of time and money in their firms; and nearly all of them are saving for their firms out of non-business income. For about half of the sample, these investments have yielded a fully-specified product; and the remainder are still in the product development stage. Family and friends are an importance source of seed money for many Nascent Entrepreneurs. Formal credit markets have been requested for funds only by a minority of Nascent Entrepreneurs, and almost half of these applicants have been denied loans. About 40% of the Nascent Entrepreneurs believe that their businesses require significantly greater equity before they can attract external funds.Business ; Business enterprises

História da ciência x aprendizagem : algumas semalhanças detectadas a partir de um estudo psicogenético sobre las idéias que evoluem para a noção de campo de força

In this article, based upon a psychogenetic study on the ideas which evolve to the concept of field of force, we show some students' conceptions which seem to be similar to others found in the History of Science. We analyse aspects which could contribute to the construction of the teaching of this concept

Competitive nucleation in metastable systems

Metastability is observed when a physical system is close to a first order phase transition. In this paper the metastable behavior of a two state reversible probabilistic cellular automaton with self-interaction is discussed. Depending on the self-interaction, competing metastable states arise and a behavior very similar to that of the three state Blume-Capel spin model is found