diff --git a/GBOpt/GBMinimizer.py b/GBOpt/GBMinimizer.py
index dd764dc..40205c4 100644
--- a/GBOpt/GBMinimizer.py
+++ b/GBOpt/GBMinimizer.py
@@ -71,7 +71,7 @@ def __init__(self, GB: GBMaker, gb_energy_func: Callable, choices: list, seed=ti
         self.manipulator.rng = self.local_random
         self.GBE_vals = []
 
-    def run_MC(self, E_accept: float = 1e-1, max_steps: int = 50, E_tol: float = 1e-4, max_rejections: int = 20, cooldown_rate: float = 1.0, unique_id: int = uuid.uuid4()) -> float:
+    def run_MC(self, E_accept: float = 1e-1, max_steps: int = 50, E_tol: float = 1e-4, max_rejections: int = 20, cooldown_rate: float = 1.0, unique_id: int | None = None) -> float:
         # TODO: Add options for changing from linear to logarithmic cooldown
         """
         Runs an MC loop on the grain boundary structure till the set convergence criteria are met.
@@ -86,6 +86,8 @@ def run_MC(self, E_accept: float = 1e-1, max_steps: int = 50, E_tol: float = 1e-
         """
 
         assert cooldown_rate > 0.0 and cooldown_rate <= 1.0
+        if unique_id is None:
+            unique_id = uuid.uuid4()
 
         # Get initial energy
         init_gbe, _ = self.gb_energy_func(
diff --git a/tests/test_mcminimizer.py b/tests/test_mcminimizer.py
new file mode 100644
index 0000000..2f87050
--- /dev/null
+++ b/tests/test_mcminimizer.py
@@ -0,0 +1,58 @@
+# Copyright 2025, Battelle Energy Alliance, LLC, ALL RIGHTS RESERVED
+
+import math
+import unittest
+import uuid
+
+import numpy as np
+
+from GBOpt.GBMaker import GBMaker
+from GBOpt.GBMinimizer import MonteCarloMinimizer
+
+
+class TestMonteCarloMinimizer(unittest.TestCase):
+    def setUp(self):
+        theta = math.radians(36.869898)
+        misorientation = np.array([theta, 0.0, 0.0, 0.0, -theta / 2.0])
+        self.gb = GBMaker(
+            3.52,
+            "fcc",
+            10.0,
+            misorientation,
+            "Ni",
+            repeat_factor=2,
+            x_dim_min=30.0,
+            vacuum=8.0,
+            interaction_distance=8.0,
+        )
+
+    def test_run_mc_default_unique_id_is_per_call(self):
+        observed_ids = []
+
+        def fake_energy_func(_gb, _manipulator, _atom_positions, unique_id):
+            observed_ids.append(unique_id)
+            return 0.0, "dummy.dump"
+
+        minimizer = MonteCarloMinimizer(
+            self.gb,
+            fake_energy_func,
+            ["insert_atoms", "remove_atoms", "translate_right_grain"],
+            seed=0,
+        )
+
+        minimizer.run_MC(max_steps=0)
+        minimizer.run_MC(max_steps=0)
+
+        self.assertEqual(len(observed_ids), 2)
+        first = observed_ids[0]
+        second = observed_ids[1]
+
+        self.assertTrue(first.startswith("initial"))
+        self.assertTrue(second.startswith("initial"))
+        first_uuid = uuid.UUID(first[len("initial"):])
+        second_uuid = uuid.UUID(second[len("initial"):])
+        self.assertNotEqual(first_uuid, second_uuid)
+
+
+if __name__ == "__main__":
+    unittest.main()