We study the recursive core introduced in Huang and Sjöström [8]. In general partition function form games, the recursive core coalition structure may be either coarser or finer than the one that maximizes the social surplus. Moreover, the recursive core structure is typically different from...

We present a method for calculating transfer matrices for the q-state Potts model partition functions Z(G,q,v), for arbitrary q and temperature variable v, on strip graphs G of the square (sq), triangular (tri), and honeycomb (hc) lattices of width Ly vertices and of arbitrarily great length Lx...

The distribution of the zeros of the partition function in the complex temperature plane (Fisher zeros) of the two-dimensional Q-state Potts model is studied for non-integer Q. On L×L self-dual lattices studied (L⩽8), no Fisher zero lies on the unit circle p0=eiθ in the complex...

We exhibit the partition function of the zero-dimensional λϕ4 model as a simple exact expression in terms of the Macdonald function for Re(λ)0. Then by analytic continuation, we obtain an expression defined in the complex coupling constant plane λ, for |argλ|<π. Consequently, the partition function understood as an analytic continuation is defined for all values of λ, except for a branch cut along the real negative λ-axis. This shows that at least in zero dimension the partition function can be defined for negative coupling constant (where the integral is formally divergent), provided it has a non-vanishing imaginary part. We also evaluate the partition function on perturbative grounds, using the Borel summation technique and we found that in the common domain of validity, for Re(λ)>0, it coincides precisely with...</π.>

We study the dissipative dynamics of a charged oscillator in a magnetic field by coupling (a la Caldeira and Leggett) it to a heat bath consisting of non-interacting harmonic oscillators. We derive here the autocorrelation functions of the position and momentum and study its behavior at various...

The Yang–Lee zeros of the Q-state Potts model are investigated in one, two and three dimensions. Analytical results derived from the transfer matrix for the one-dimensional model reveal a systematic behavior of the locus of zeros as a function of Q. For 1<Q<2 the zeros in the complex x=exp(βHq) plane lie inside the unit circle, while for Q>2 they lie outside the unit circle for...</q<2>

This paper revisits the fundamental statistical properties of the crucial model in critical phenomena i.e., the Ising model, guided by our knowledge of the energy values of the Ising Hamiltonian and aided by numerical estimation techniques. We have obtained exact energies in 2D and 3D and nearly...

We seek the numerical calculation of partition functions of general Markov random fields (MRFs) on an infinitely long twisted cylindrical lattice by using the transfer-matrix renormalization group (TMRG) method. The TMRG is a variant of the density-matrix renormalization group (DMRG) which...

In the model of Funaki and Yamato (1999) the tragedy of the commons can be avoided with pessimistic players, while this does not hold for optimistic players. We propose a new core concept to overcome this puzzle and provide numerical simulations of simple games where the conclusions coincide or...

We consider partition function games and introduce new defini-tions of the core that include the effects of externalities. We assume that all players behave rationally and that all stable outcomes arising are consistent with the appropriate generalised concept of the core. The result is a...