2,700 research outputs found
Overfrustrated and Underfrustrated Spin-Glasses in d=3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d=2
In spin-glass systems, frustration can be adjusted continuously and
considerably, without changing the antiferromagnetic bond probability p, by
using locally correlated quenched randomness, as we demonstrate here on
hypercubic lattices and hierarchical lattices. Such overfrustrated and
underfrustrated Ising systems on hierarchical lattices in d=3 and 2 are
studied. With the removal of just 51 % of frustration, a spin-glass phase
occurs in d=2. With the addition of just 33 % frustration, the spin-glass phase
disappears in d=3. Sequences of 18 different phase diagrams for different
levels of frustration are calculated in both dimensions. In general,
frustration lowers the spin-glass ordering temperature. At low temperatures,
increased frustration favors the spin-glass phase (before it disappears) over
the ferromagnetic phase and symmetrically the antiferromagnetic phase. When any
amount, including infinitesimal, frustration is introduced, the chaotic
rescaling of local interactions occurs in the spin-glass phase. Chaos increases
with increasing frustration, as seen from the increased positive value of the
calculated Lyapunov exponent , starting from when
frustration is absent. The calculated runaway exponent of the
renormalization-group flows decreases with increasing frustration to
when the spin-glass phase disappears. From our calculations of entropy and
specific heat curves in d=3, it is seen that frustration lowers in temperature
the onset of both long- and short-range order in spin-glass phases, but is more
effective on the former. From calculations of the entropy as a function of
antiferromagnetic bond concentration p, it is seen that the ground-state and
low-temperature entropy already mostly sets in within the ferromagnetic and
antiferromagnetic phases, before the spin-glass phase is reached.Comment: Published version, 18 phase diagrams, 12 figures, 10 page
Odd q-State Clock Spin-Glass Models in Three Dimensions, Asymmetric Phase Diagrams, and Multiple Algebraically Ordered Phases
Distinctive orderings and phase diagram structures are found, from
renormalization-group theory, for odd q-state clock spin-glass models in d=3
dimensions. These models exhibit asymmetric phase diagrams, as is also the case
for quantum Heisenberg spin-glass models. No finite-temperature spin-glass
phase occurs. For all odd , algebraically ordered
antiferromagnetic phases occur. One such phase is dominant and occurs for all
. Other such phases occupy small low-temperature portions of the
phase diagrams and occur for . All algebraically
ordered phases have the same structure, determined by an attractive
finite-temperature sink fixed point where a dominant and a subdominant pair
states have the only non-zero Boltzmann weights. The phase transition critical
exponents quickly saturate to the high q value.Comment: Published version, 9 pages, 10 phase diagrams, 5 figures, 1 tabl
The measurement of opportunity inequality: a cardinality-based approach
We consider the problem of ranking distributions of opportunity sets on the basis of equality. First, conditional on agents' preferences over individual opportunity sets, we formulate the analogues ofthe notions ofthe Lorenz partial ordering, equalizing Dalton transfers, and inequality averse social welfare functionals -concepts which play a central role in the literature on income inequality. For the particular case in which agents rank opportunity sets on the basis of their cardinalities, we establish an analogue of the fundamental theorem of inequality measurement: one distribution Lorenz dominates another if and only if the former can be obtained from the latter by a finite sequence of equalizing transfers, and if and only if the former is ranked higher than the latter by all inequality averse social welfare functionals. In addition, we characterize the smallest monotonic and transitive extension of the cardinality-based Lorenz inequality ordering
The measurement of opportunity inequality: a cardinality-based approach.
We consider the problem of ranking distributions of opportunity sets on the basis of equality. First, conditional on agents' preferences over individual opportunity sets, we formulate the analogues ofthe notions ofthe Lorenz partial ordering, equalizing Dalton transfers, and inequality averse social welfare functionals -concepts which play a central role in the literature on income inequality. For the particular case in which agents rank opportunity sets on the basis of their cardinalities, we establish an analogue of the fundamental theorem of inequality measurement: one distribution Lorenz dominates another if and only if the former can be obtained from the latter by a finite sequence of equalizing transfers, and if and only if the former is ranked higher than the latter by all inequality averse social welfare functionals. In addition, we characterize the smallest monotonic and transitive extension of the cardinality-based Lorenz inequality ordering.Opportunity Inequality; Equalizing Transfers; Lorenz Domination;
Delay aversion
We address the following question: When can one person properly be said to be more delay averse than another? In reply, several (nested) comparison methods are developed. These methods yield a theory of delay aversion which parallels that of risk aversion. The applied strength of this theory is demonstrated in a variety of dynamic economic settings, including the classical optimal growth and tree cutting problems, repeated games, and bargaining. Both time-consistent and time-inconsistent scenarios are considered.Delay aversion, impatience, consumption smoothing, time consistency
On the Strategic Advantage of Negatively Interdependent Preferences
We study certain classes of supermodular and submodular games which are symmetric with respect to material payoffs but in which not all players seek to maximize their material payoffs. Specifically, a subset of players have negatively interdependent preferences and care not only about their own material payoffs but also about their payoffs relative to others. We identify sufficient conditions under which members of the latter group have a strategic advantage in the following sense: at all intragroup symmetric equilibria of the game, they earn strictly higher material payoffs than do players who seek to maximize their material payoffs. We show that these conditions are satisfied by a number of games of economic importance, and discuss the implications of these findings for the evolutionary theory of preference formation and the theory of Cournot competition.Interdependent Preferences, Submodular and Supermodular Games, Relative Profits, Cournot Oligopoly
Expected Utility Theory without the Completeness Axiom
We study axiomatically the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteries by means of a set of von Neumann-Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a well-defined sense.Expected utility, incomplete preferences
Interdependent Preference Formation
A standard assumption in the economic approach to individual decision making is that people have independent preferences, that is, they care only about their absolute (material) payoffs. We study equilibria of the classic common pool resource extraction and public good games when some of the players have negatively interdependent preferences (in the sense that they care not only about their absolute payoffs but also about their relative payoffs) while the remainder have independent preferences. It is shown that at any equilibrium, those with interdependent preferences earn strictly higher absolute payoffs than do players with independent preferences. If the population composition evolves in accordance with any payoff monotonic evolutionary selection dynamics, then all players will have interdependent preferences in the long run. Similar (but weaker) results obtain for some other economically important classes of games in strategic form. The robustness of our findings with respect to other preference formation mechanisms such as myopic and rational socialization is also discussed.Interdependent Preferences, Evolution, Socialization.
Stochastic Dominance in Mobility Analysis
This paper introduces a technique for mobility dominance and compares the degree of earnings mobility of men in the USA from 1970 to 1995. The highest mobility is found in the 1975–1980 or 1980–1985 periods
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