Abstract
We study the possibility to implement the canonical Tsallis distribution for lattice field theory simulations. Formally, the application of the Tsallis distribution can be interpreted as introducing a fluctuating temperature. We give arguments for the approach and present our simulation method as well as our first numerical results in determining the equation of state for pure SU(2) lattice gauge fields.
Highlights
If E denotes the energy of a state of the system, the Tsallis distribution is given with the probability distribution w(E) = 1 1 + βE −c (1) ZT S c(β is the inverse temperature)
We study the possibility to implement the canonical Tsallis distribution for lattice field theory simulations
The application of the Tsallis distribution can be interpreted as introducing a fluctuating temperature
Summary
If E denotes the energy of a state of the system, the Tsallis distribution is given with the probability distribution w(E) = 1 1 + βE −c (1). The quantity q = 1 + 1/c is the Tsallis index. It is easy to show that the following identity holds:. The identity (3) is remarkable: it shows that averages with the Tsallis distribution can be evaluated as averaging over different β valued Gibbs expectation values. This is a specific example of the superstatistical approach [20], where the inverse temperature is not a simple quantity: it follows a Gamma distribution
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