Final answer:
The specific term 'hammer and fist' does not appear in historical records regarding the Persian forces at the Battle of Thermopylae. Instead, the Persian army included a variety of troops, with the elite unit known as the Immortals being the most famous.
Step-by-step explanation:
The question pertains to a particular Persian fighting force who were engaged in combat with the Spartans on the second day of the Battle of Thermopylae in 480 BCE. However, the provided information does not mention a specifically named "hammer and fist" fighting force. Throughout the historical accounts of Herodotus and other ancient historians, mention of the Immortals, an elite infantry group, exists, but they were not specifically identified by this term. The Persian army at Thermopylae was comprised of various ethnic groups and included a blend of infantry, archers, and cavalry but without a distinct designation as 'hammer and fist'. The Battle of Thermopylae, as part of the Greco-Persian Wars, was noted for the heroic stand of the vastly outnumbered Greeks, particularly the Spartans under King Leonidas, against the much larger Persian forces of King Xerxes I.