Question

In the paper Inverse statistical problems: from the inverse Ising problem to data science for equation (51), the authors state, "This yields equations which determine the values mMFi of the magnetization parameters that minimize the KL divergence between the mean-field ansatz and the Boltzmann distribution, namely the well-known self-consistent equations m^M^F i = th (hᵢ + ∑ⱼ_≠ᵢ Jᵢⱼm^M^F j )" Does the 'th' here simply mean some Gibbs type of distribution i.e. e⁻^β(.) for some th(.)?

Answer 1

The 'th' in the equation refers to the hyperbolic tangent function, which is commonly denoted as th or tanh. It is used to calculate the self-consistent magnetization parameters that minimize the Kullback-Leibler divergence between the mean-field ansatz and the Boltzmann distribution.

Step-by-step explanation:

The 'th' in the equation refers to the hyperbolic tangent function, which is commonly denoted as th or tanh.

The hyperbolic tangent function is often used in statistical physics and describes the relationship between the magnetic field and magnetization in systems.

In this equation, it is used to calculate the self-consistent magnetization parameters that minimize the Kullback-Leibler divergence between the mean-field ansatz and the Boltzmann distribution.