{"knowledge_schema": {"broad_category": "Statistical Mechanics \u2192 Thermodynamics \u2192 Partition Function", "refinement": "This problem involves calculating the partition function for a system of three interacting spins, taking into account their possible configurations and corresponding energies.", "specific_scope": "The focus is on a system of three spins, each with two possible states (+1 or -1), and the energy defined by a specific interaction term involving a coupling constant J.", "goal": "Calculate the partition function Z by summing over all possible configurations of the spins and their associated Boltzmann factors."}, "summary": "In this problem, we are tasked with calculating the partition function Z for a system of three spins, each of which can be in one of two states (+1 or -1). The energy of the system is defined by the interaction between the spins, and we need to consider all possible configurations to compute Z. The correct answer is Z = 2 e^(3J\u03b2) + 6 e^(-J\u03b2), which accounts for the different energy states of the system based on the spins' configurations."}