{"knowledge_schema": {"broad_category": "Statistical Mechanics \u2192 Thermodynamics \u2192 Partition Function", "refinement": "This problem involves calculating the partition function for a system of three spins, each of which can take on two possible states (+1 or -1), and determining the energy associated with each configuration of spins.", "specific_scope": "The focus is on evaluating the partition function Z for a specific energy expression involving interactions between the spins, using the Boltzmann factor to account for the probabilities of each configuration at a given temperature.", "goal": "Calculate the partition function Z by summing over all possible configurations of the spins and their corresponding energies."}, "summary": "In this problem, we are tasked with finding the partition function Z for a system of three spins, each capable of being in states +1 or -1. The energy of the system is defined by the interaction between the spins. To find Z, we need to consider all possible configurations of the spins, calculate their energies, and apply the Boltzmann factor to each configuration. The correct answer is Z= 2 e^(3J\u03b2)+6e^(-J\u03b2), which accounts for the contributions from all configurations of the spins."}