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We provide a mathematical model to investigate the human resource allocationproblem for agents, say, university graduates who are looking for theirpositions in labor markets. The basic model is described by the so-called Pottsspin glass which is well-known in the research field of statistical physics. Inthe model, each Potts spin (a tiny magnet in atomic scale length) representsthe action of each student, and it takes a discrete variable corresponding tothe company he/she applies for. We construct the energy to include threedistinct effects on the students' behavior, namely, collective effect, markethistory and international ranking of companies. In this model system, thecorrelations (the adjacent matrix) between students are taken into accountthrough the pairwise spin-spin interactions. We carry out computer simulationsto examine the efficiency of the model. We also show that some chiralrepresentation of the Potts spin enables us to obtain some analytical insightsinto our labor markets.

Statistical mechanics of human resource allocation: A mathematical modeling of job-matching in labor markets