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We study the violations of Bell inequality for thermal states of qubits in amulti-qubit Heisenberg model as a function of temperature and external magneticfields. Unlike the behaviors of the entanglement the violation can not beobtained by increasing the temperature or the magnetic field. The thresholdtemperatures of the violation are found be less than that of the entanglement.We also consider a realistic cavity-QED model which is a special case of themutli-qubit Heisenberg model.Comment: 5 pages, 5 figures, few changed, accepted by New J. Phy

Violation of the Bell inequality for thermal states of interaction qubits investigated via a multi-qubit Heisenberg model