446 research outputs found
General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
We examine critically the issue of phase transitions in one-dimensional
systems with short range interactions. We begin by reviewing in detail the most
famous non-existence result, namely van Hove's theorem, emphasizing its
hypothesis and subsequently its limited range of applicability. To further
underscore this point, we present several examples of one-dimensional short
ranged models that exhibit true, thermodynamic phase transitions, with
increasing level of complexity and closeness to reality. Thus having made clear
the necessity for a result broader than van Hove's theorem, we set out to prove
such a general non-existence theorem, widening largely the class of models
known to be free of phase transitions. The theorem is presented from a rigorous
mathematical point of view although examples of the framework corresponding to
usual physical systems are given along the way. We close the paper with a
discussion in more physical terms of the implications of this non-existence
theorem.Comment: Short comment on possible generalization to wider classes of systems
added; accepted for publication in Journal of Statistical Physic
The Shared Reward Dilemma
One of the most direct human mechanisms of promoting cooperation is rewarding
it. We study the effect of sharing a reward among cooperators in the most
stringent form of social dilemma, namely the Prisoner's Dilemma. Specifically,
for a group of players that collect payoffs by playing a pairwise Prisoner's
Dilemma game with their partners, we consider an external entity that
distributes a fixed reward equally among all cooperators. Thus, individuals
confront a new dilemma: on the one hand, they may be inclined to choose the
shared reward despite the possibility of being exploited by defectors; on the
other hand, if too many players do that, cooperators will obtain a poor reward
and defectors will outperform them. By appropriately tuning the amount to be
shared a vast variety of scenarios arises, including traditional ones in the
study of cooperation as well as more complex situations where unexpected
behavior can occur. We provide a complete classification of the equilibria of
the -player game as well as of its evolutionary dynamics.Comment: Major rewriting, new appendix, new figure
Altruistic behavior pays, or the importance of fluctuations in evolutionary game theory
Human behavior is one of the main problems for evolution, as it is often the
case that human actions are disadvantageous for the self and advantageous for
other people. Behind this puzzle are our beliefs about rational behavior, based
on game theory. Here we show that by going beyond the standard game-theoretical
conventions, apparently altruistic behavior can be understood as
self-interested. We discuss in detail an example related to the so called
Ultimatum game and illustrate the appearance of altruistic behavior induced by
fluctuations. In addition, we claim that in general settings, fluctuations play
a very relevant role, and we support this claim by considering a completely
different example, namely the Stag-Hunt game.Comment: For the proceedings of the 8th Granada Seminar on Computational
Physics (AIP Proceedeings Series
Emergence and resilience of cooperation in the spatial Prisoner's Dilemma via a reward mechanism
We study the problem of the emergence of cooperation in the spatial
Prisoner's Dilemma. The pioneering work by Nowak and May showed that large
initial populations of cooperators can survive and sustain cooperation in a
square lattice with imitate-the-best evolutionary dynamics. We revisit this
problem in a cost-benefit formulation suitable for a number of biological
applications. We show that if a fixed-amount reward is established for
cooperators to share, a single cooperator can invade a population of defectors
and form structures that are resilient to re-invasion even if the reward
mechanism is turned off. We discuss analytically the case of the invasion by a
single cooperator and present agent-based simulations for small initial
fractions of cooperators. Large cooperation levels, in the sustainability
range, are found. In the conclusions we discuss possible applications of this
model as well as its connections with other mechanisms proposed to promote the
emergence of cooperation
Rewarding cooperation in social dilemmas
One of the most direct human mechanisms of promoting cooperation is rewarding it. We study the effect of sharing a reward among cooperators in the most stringent form of social dilemma. Thus, individuals confront a new dilemma: on the one hand, they may be inclined to choose the shared reward despite the possibility of being exploited by defectors; on the other hand, if too many players do that, cooperators will obtain a poor reward and defectors will outperform them. By appropriately tuning the amount to be shared we can cast a vast variety of scenarios, including traditional ones in the study of cooperation as well as more complex situations where unexpected behavior can occur. We provide a complete classification of the equilibria of the nplayer game as well as of the evolutionary dynamics. Beyond, we extend our analysis to a general class of public good games where competition among individuals with the same strategy exists.
Potential models for the simulation of methane adsorption on graphene: development and CCSD(T) benchmarks
Different force fields for the graphene–CH4 system are proposed including pseudo-atom and full atomistic models. Furthermore, different charge schemes are tested to evaluate the electrostatic interaction for the CH4 dimer. The interaction parameters are optimized by fitting to interaction energies at the DFT level, which were themselves benchmarked against CCSD(T) calculations. The potentials obtained with both the pseudo-atom and full atomistic approaches describe accurately enough the average interaction in the methane dimer as well as in the graphene–methane system. Moreover, the atom–atom potentials also correctly provide the energies associated with different orientations of the molecules. In the atomistic models, charge schemes including small charges allow for the adequate representation of the stability sequence of significant conformations of the methane dimer. Additionally, an intermediate charge of −0.63e on the carbon atom in methane leads to bond energies with errors of ca. 0.07 kcal mol−1 with respect to the CCSD(T) values for the methane dimer. For the graphene–methane interaction, the atom–atom potential model predicts an average interaction energy of 2.89 kcal mol−1, comparable to the experimental interaction energy of 3.00 kcal mol−1. Finally, the presented force fields were used to obtain self-diffusion coefficients that were checked against the experimental value found in the literature. The no-charge and Hirshfeld charge atom–atom models perform extremely well in this respect, while the cheapest potential considered, a pseudo-atom model without charges, still performs reasonably well
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