TL;DR
This paper introduces the concept of ground subgroups in finite and countable groups, exploring their properties and applications in describing ground states in statistical mechanics models.
Contribution
It defines ground subgroups based on subsets and partitions, and characterizes their sets for finite and free groups, applying them to statistical mechanics.
Findings
Defined ground subgroups depending on subsets and partitions.
Described sets of ground subgroups for finite and free groups.
Applied ground subgroups to model ground states in statistical mechanics.
Abstract
In this article we give a concept of ground subgroup for finite and countable groups. By our definition such a subgroup of a group depends on a given subset of the group and on a given partition of the subset. For finite and free groups we describe some sets of ground subgroups. We apply the ground subgroups to describe ground states of a model of statistical mechanics.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Limits and Structures in Graph Theory