diff --git a/Exercise sheet 6/exercise_sheet_06.ipynb b/Exercise sheet 6/exercise_sheet_06.ipynb
index 7f91a32..a75cfc7 100644
--- a/Exercise sheet 6/exercise_sheet_06.ipynb	
+++ b/Exercise sheet 6/exercise_sheet_06.ipynb	
@@ -257,7 +257,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 82,
+   "execution_count": 100,
    "id": "6e4a6d63",
    "metadata": {
     "deletable": false,
@@ -288,7 +288,7 @@
     "    unvisited = deque([seed])\n",
     "    while unvisited:\n",
     "        site = unvisited.pop()\n",
-    "        s_i_n = -np.dot(state[site], nhat)\n",
+    "        s_i_n = -state[site]@nhat\n",
     "        for nbr in neighboring_sites(site,w):\n",
     "            s_j_n = state[nbr]@nhat\n",
     "            p_add = 1 - np.exp(-2*beta*s_i_n*s_j_n)\n",
@@ -308,7 +308,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 83,
+   "execution_count": 101,
    "id": "3f810041",
    "metadata": {
     "deletable": false,
@@ -339,7 +339,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 84,
+   "execution_count": 102,
    "id": "bde560e4",
    "metadata": {
     "deletable": false,