The Statistical Physics of Psychological Networks: Zero Matters

Psychological network theories provide an important alternative to traditional common cause theories, such as the g-theory of general intelligence and brain-based explanations of depression. Network theories, which are often formalized using the Ising model from statistical physics, have gained significant empirical support. However, the binary nature of nodes in Ising-type models presents a limitation, as many psychological datasets include responses with uncertain or neutral categories (e.g., "don't know" or "not relevant"). Ternary spin models, such as the Blume-Capel model, overcome this constraint by incorporating a third node state, zero, that can represent such responses, enabling more nuanced scale representations. The resulting models exhibit more complex dynamics and provide new insights into research across a range of psychological constructs. We illustrate our approach with examples from three key subdisciplines of psychology. First, we introduce a ternary spin model for attitudes, extending the Ising attitude model. Next, we propose a unified framework encompassing both bipolar disorder and major depressive disorder. Finally, we present a novel ternary network model for understanding knowledge acquisition.